CN115102847B - Self-adaptive event triggering fault detection method for network system - Google Patents

Abstract

The invention provides a self-adaptive time departure fault detection method of a network system, which utilizes a positive semi-Markov system to establish a state space model of the network system. By means of linear Lyapunov function and matrix decomposing technology, the fault detecting device is designed with the filter to avoid faults, jamming and other problems effectively. Based on the self-adaptive event triggering mechanism, the occurrence point of the next moment is actively predicted at the triggering moment according to the previously received data and the system dynamics, so that the phenomenon of network congestion is effectively relieved, and the waste of network resources is reduced.

Description

Self-adaptive event triggering fault detection method for network system

Technical Field

The invention belongs to the field of automation technology and modern control, and particularly relates to a self-adaptive event-triggered fault detection method of a network system.

Background

As for control systems in a network environment, networked control systems were proposed as early as the 80 s of the last century and developed rapidly in a later period. Compared with the traditional point-to-point control system, the networked control system has limited information resource sharing, low cost, flexible expansion and the like, and is gradually widely used in life due to the development of high and new technology industry and electronic communication technology in recent years.

In network communications, information is divided into a plurality of data blocks (packets) that are transmitted along different paths in one or more networks and reassembled at a destination. Since the number of data packets is non-negative, the network system conforms to the characteristics of a positive system. Because of the complexity of the network environment, the network system can be divided into two states of busy and idle according to the number of data packets received by each network node, and the network system performs random switching between the two modes, and the states of the network system remain non-negative. Thus, the network system can be modeled as a positive semi-markov system. In addition, the practically applied system is not completely linear, and if the nonlinearity in some parts of the system is modeled as a linear system, a certain control precision is lost, so that a certain degree of nonlinearity factor needs to be added for modeling consideration while research is performed. Fault detection refers to determining whether a system has failed by technically analyzing a measurement signal of the system, such as a residual signal. The sensitivity to faults is one of main evaluation indexes of fault detection.

Due to the introduction of the network, the phenomena of network blockage, resource waste and the like exist when data are transmitted in a network environment. The proposal of the event triggering mechanism enables the system to reduce the number of transmitted data packets and effectively alleviate the problem on the premise of ensuring certain performance and stability. In practical hardware detection circuits, an interrupt signal is often used to control when data is released and updated, but for an already designed system, adding an event trigger is often inappropriate, so an adaptive event trigger mechanism is generated. Unlike active event triggering mechanisms, adaptive triggering mechanisms are passively triggered, requiring active prediction of the point of occurrence at the next moment at the moment of triggering, based on previously received data and system dynamics.

In conclusion, the self-adaptive event triggering fault detection method of the network system based on nonlinear positive Markov system modeling has important scientific research significance and practical application significance.

Disclosure of Invention

The self-adaptive event triggering fault detection method of the network system aims at solving the problems of faults, congestion and the like of the network system, researching the network control system and providing the self-adaptive event triggering fault detection method of the network system.

In order to solve the technical problems, the technical scheme of the invention is as follows:

An adaptive event triggering fault detection method of a network system comprises the following steps:

s1, establishing a nonlinear positive half Markov system state space model of a network control system

S1-1, establishing a state space model of a network control system

Wherein,System state, system input and system output, respectively; Representing an additional disturbance located in L ₁ [0, +#); /(I) Is a fault signal to be detected in L ₁ [0, ]; /(I)And/>Is a non-linearity of the system; g _b (u (t)) is defined as g _b (w (t)), the system matrix is denoted by A _i,B_i,C_i,D_i,E_i,F_i, where i εS;

S1-2, converting into nonlinear positive semi-Markov system state space model

In probability spaceThe semi-Markov process { r _t, t.gtoreq.0 } defined above is a right-hand continuous process and is performed in a finite set S= {1,2, …, N },/>For values i not equal to j and q _ii =0, let/>Is a homogeneous markov update process, where t _k represents the kth jump instant, { X _k } is the associated state in the markov chain, the transition probability is q _ij＝P_r{X_k+1＝j|X_k =i }, the time interval between two consecutive jumps τ _k＝t_k-t_k-1 is the dwell time of the semi-markov process { r _t}_t≥0,

Wherein h is greater than or equal to 0 andBy calculation, there is/>And lambda _ij (h) is the transfer rate corresponding to the mode i from time t to time t+delta at mode j, lambda _ij (h) >0 (i not equal to j), andLet us assume that the transition probability of the semi-markov process r _t satisfies/>

S2, constructing an actuator fault model;

S3, constructing a self-adaptive event triggering strategy;

S4, constructing a new fault signal;

s5, constructing a fault detection filter under the event triggering condition;

s6, constructing a nonlinear function condition;

S7, setting a condition for stable operation of the network fault detection system.

Preferably, in the step S2, the actuator fault model is constructed as follows:

Wherein, Representing failure modes belonging to a model set: q= {1,2, …, L } and/>Representing the total number of failure modes, a defined diagonal matrix/>Defined as/> Diagonal element/>Is 1 or 0,I is an identity matrix of known dimensions.

Preferably, in the step S3, the adaptive event trigger policy is constructed as follows:

Let t _ι be the iota event trigger time, define the event trigger error function as: Where m (t) is the sampling error,/> The event triggering condition is constructed as follows:

||m(t)||₁>β(t)||y(t)||₁,

Wherein the adaptive event trigger coefficient β (t) satisfies:

wherein, Λ, beta (0), Are all predefined constants.

Preferably, in the step S4, the method for constructing the fault signal is as follows:

The minimum implementation of f _w (t) to estimate the original fault by detecting a new fault signal is given by:

f_w(t)＝C_wg_a(x_w(t))+D_wf(t),

Wherein, Is a weighted failure state,/>Is an original failure,/>Is a weighted fault, a _w,B_w,C_w,D_w is a known matrix with the appropriate dimensions.

Preferably, in the step S5, the fault detection filter under the event triggering condition is constructed as follows:

Wherein, Is the state vector of the filter,/>Representing residual signal,/>Representing the filter input, defined in probability space/>The upper half Markov process { delta _t, t.gtoreq.0 } is a right continuous process, the finite set of values S= {1,2, …, N },/>And/>Denoted as A _fl,B_fl,C_fl,D_fl is the filter matrix to be determined, the relationship between the system pattern r _t and the filter pattern delta _t can be described by a conditional probability matrix Y= { θ _il }, where P _r{δ_t＝l|r_t＝i}＝θ_il, where for each i ε S,/>

Definition of the definitionE (t) =r _f(t)-f_w (t), an extended fault detection system is obtained as follows:

Wherein,

Introducing a fault detection mechanism of a residual evaluation function: Where T represents the evaluation time, J _r (T) is the residual evaluation function, and depending on the residual evaluation function selected, the threshold may be defined as:

wherein the method comprises the steps of The fault detection scheme that indicates that all disturbance inputs of L ₁ -norm are in the interval [0, ++), and that determines whether a fault has occurred, can be configured to:

preferably, the nonlinear function condition in the step S6 is constructed as follows:

the nonlinear functions g _a (x (t)) and g _b (x (t)) satisfy the following sector conditions:

Wherein 1.ltoreq.i.ltoreq.n, 0< iota ₁<ι₂,0<κ₁<κ₂ and g _ai(0)＝0,g_bi (0) =0.

Preferably, in the step S7, the steady operation condition of the fault detection system is set as follows:

the design constant a >0 is chosen, Λ>0,γ_w>0,γ_f>0,σ>0,c₁>0,ι₂>0,κ₁>0,κ₂>0,/>Vector quantity And/>Vector quantity So that

α≥nσ,

For any μ=1, 2, …, n and v=1, 2, …, q, the fault detection system is positive, randomly stable and meets the L ₁ gain performance under the event triggered filter in step S4, where,And/>The gain matrix satisfies

Preferably, the method further comprises the step of step S8 of verification:

S8-1, positive verification of a fault detection system;

s8-2, verifying random stability of a fault detection system;

s8-3, the sensitivity of the event triggering filter to the fault detection system is verified.

Preferably, in the step S8-1, the positive verification method of the fault detection system is as follows:

S8-1-1, consider when in network fault detection system And f (t) =0, using the adaptive event triggering strategy in step S3, one can derive

For any initial conditionsNote/>Then the first time period of the first time period,

S8-1-2, the extended fault detection system in step S5 and step S8-1-1, for any non-negative initial conditions, result

Wherein,

Can be given according to the conditions in step S7Then,/>Furthermore, A _il is Metzer andThus, the network failure detection system is positive.

Preferably, in the step S8-2, the method for verifying the random stability of the fault detection system is as follows:

S8-2-1, the selected Lyapunov function is as follows:

by using the step 8-1-1, it is possible to obtain

Wherein the method comprises the steps of

S8-2-2, thereby obtaining

S8-2-3, in combination with the conditions in step S7

S8-2-4, using step S8-2-3, the following inequality holds:

this means

S8-2-5, under zero initial value, get

And then obtain

Thus (2)

Thus, the fault detection system is randomly stable and has a hybrid L ₁ gain performance.

Preferably, in the step S8-3, the method for verifying sensitivity of the event triggered filter to the fault detection system is as follows:

S8-3-1, setting a condition for stable operation of the fault detection system, wherein the setting method is the same as that of the step S7;

S8-3-2, the verification event triggering filter is sensitive to faults, and comprises positive verification of a network fault detection system and verification of random stability of the network fault detection system, wherein the verification method is the same as that of the step S8-1 and the step S8-2.

The invention has the following characteristics and beneficial effects:

first, a state space model of a network system is established by using a positive semi-Markov system. By means of linear Lyapunov function and matrix decomposing technology, the fault detecting device is designed with the filter to avoid faults, jamming and other problems effectively. Based on the self-adaptive event triggering mechanism, the occurrence point of the next moment is actively predicted at the triggering moment according to the previously received data and the system dynamics, so that the phenomenon of network congestion is effectively relieved, and the waste of network resources is reduced.

Drawings

In order to more clearly illustrate the embodiments of the invention or the technical solutions of the prior art, the drawings which are used in the description of the embodiments or the prior art will be briefly described, it being obvious that the drawings in the description below are only some embodiments of the invention, and that other drawings can be obtained according to these drawings without inventive faculty for a person skilled in the art.

Fig. 1 is a diagram of an adaptive event-triggered failure detection framework for a positive semi-markov transition system of an embodiment of the present invention.

Fig. 2 is a schematic diagram of a network communication process applied to an embodiment of the present invention.

Detailed Description

It should be noted that, without conflict, the embodiments of the present invention and features of the embodiments may be combined with each other.

The invention provides a self-adaptive event triggering fault detection method of a network system, as shown in fig. 1 and 2, comprising the following specific steps:

s1, establishing a nonlinear positive half Markov system state space model of a network control system, wherein the specific method comprises the following steps:

s1-1, establishing a state space model of a network control system

Wherein,System state, system input and system output, respectively; Representing an additional disturbance located in L ₁ [0, +#); /(I) Is a fault signal to be detected in L ₁ [0, ]; /(I)And/>Is a non-linearity of the system; g _b (u (t)) is defined as g _b (w (t)).

S1-2, converting into nonlinear positive semi-Markov system state space model

In probability spaceThe semi-Markov process { r _t, t.gtoreq.0 } defined above is a right-hand continuous process and is performed in a finite set S= {1,2, …, N },/>And (3) taking the value. For i+.j and q _ii =0, let/>Is a homogeneous markov update process, where t _k represents the kth jump instant, { X _k } is the associated state in the markov chain, and the transition probability is q _ij＝P_r{X_k+1＝j|X_k =i }. The time interval τ _k＝t_k-t_k-1 between two consecutive hops is the dwell time of the semi-markov process { r _t}_t≥0.

Wherein h is greater than or equal to 0 andBy simple calculation, there is/>And lambda _ij (h) is the transfer rate corresponding to the mode i from time t to time t+delta at mode j, lambda _ij (h) >0 (i not equal to j), andLet us assume that the transition probability of the semi-markov process r _t satisfies/>For simplicity, the system matrix is denoted by A _i,B_i,C_i,D_i,E_i,F_i for i εS. Assume a _i is Metzler and is non-negative.

In particular, the probability distribution of the residence time is described by a Weibull distribution, wherein the cumulative distribution function and the probability distribution function of the Weibull distribution are as follows:

where ρ >0 is a scale parameter and ν >0 is a shape parameter. The conversion rate function is then expressed as

S2, constructing an actuator fault model, wherein the construction form is as follows:

Wherein, Representing failure modes belonging to a model set: q= {1,2, …, L } and/>Representing the total number of failure modes. Prescribed diagonal matrix/>Defined as/> Diagonal element/>Is 1 or 0,I is an identity matrix of known dimensions.

It will be appreciated that ifThen/>This means that no failure occurs. When/>And f _k (t) noteq0, the kth actuator fails. Then, the nonlinear positive semi-Markov system state space model in step S1-1 can be described as:

y(t)＝C_ig_a(x(t))+D_ig_b(w(t))+F_if(t)

Wherein,

S3, constructing a self-adaptive event triggering strategy

Let t _ι be the iota event trigger time. Defining an event trigger error function as: Wherein, The event triggering condition is constructed as follows:

||m(t)||₁>β(t)||y(t)||₁,

Wherein the adaptive event trigger coefficient β (t) satisfies:

wherein, Λ, beta (0), Are all predefined constants.

S4, constructing a new fault signal, wherein the construction form is as follows:

The original fault is estimated by detecting a new fault signal. Here, the minimum implementation of f _w (t) is given by:

f_w(t)＝C_wg_a(x_w(t))+D_wf(t),

Wherein, Is a weighted failure state,/>Is an original failure,/>Is a weighted fault, a _w,B_w,C_w,D_w is a known matrix with the appropriate dimensions.

S5, constructing a fault detection filter under the event triggering condition, wherein the form is as follows:

Wherein, Is the state vector of the filter,/>Representing residual signal,/>Representing the filter input. Defined in probability space/>The upper half Markov process { delta _t, t.gtoreq.0 } is a right continuous process, the finite set of values S= {1,2, …, N },/>And/>Denoted a _fl,B_fl,C_fl,D_fl is the filter matrix to be determined. Furthermore, the relationship between the system mode r _t and the filter mode δ _t can be described by a conditional probability matrix y= { θ _il }, where P _r{δ_t＝l|r_t＝i}＝θ_il, where for each i e S,/>

It can be seen that the jump procedure for filter delta _t is different from that for system r _t. This means that the designed filter is an asynchronous filter, which is more practical than a synchronous filter.

Further, defineE (t) =r _f(t)-f_w (t). An extended fault detection system is obtained as follows:

Wherein,

Introducing a fault detection mechanism of a residual evaluation function: Where T represents the evaluation time and J _r (T) is the residual evaluation function. According to the selected residual evaluation function, the threshold may be defined as:

wherein the method comprises the steps of Indicating that L ₁ -norm all interfering inputs are on interval 0, ++). The fault detection scheme for judging whether a fault occurs may be configured as:

s6, constructing nonlinear function conditions, wherein the nonlinear function conditions are as follows:

the nonlinear functions g _a (x (t)) and g _b (x (t)) satisfy the following sector conditions:

Wherein 1.ltoreq.i.ltoreq.n, 0< iota ₁<ι₂,0<κ₁<κ₂ and g _ai(0)＝0,g_bi (0) =0.

S7, designing the condition of stable operation of the network fault detection system as follows:

the design constant a >0 is chosen, Λ>0,γ_w>0,γ_f>0,σ>0,ι₁>0,ι₂>0,κ₁>0,κ₂>0,/>Vector quantity And/>Vector quantity So that

/>

α≥nσ,

For any μ=1, 2, …, n and v=1, 2, …, q, then the network failure detection system is positive, randomly stable and meets the L ₁ gain performance under the event triggered filter in step S5, where,AndThe gain matrix satisfies

S8, verifying

S8-1, a positive verification process of the network fault detection system is as follows:

S8-1-1, first, consider when in the network failure detection system And f (t) =0. Using the adaptive event triggering strategy in step S3, one can derive

For any initial conditionsNote/>Then the first time period of the first time period,

S8-1-2, the extended fault detection system in step S5 and step S8-1-1, for any non-negative initial conditions, result

Wherein,

C_il＝(E_flZ₁C_i C_fl D_fl-C_w),D_il＝(0 E_flZ₁D_i),E_il＝E_flZ₁F_i-D_w.

Can be given according to the conditions in step S7Then,/>Furthermore, A _il is Metzer and/>Thus, the network failure detection system is positive.

S8-2, the random stability verification process of the network fault detection system is as follows:

S8-2-1, the selected Lyapunov function is as follows:

By using the step S8-1-1, it is possible to obtain

Wherein the method comprises the steps of

S8-2-2, then,

S8-2-3, in combination with the conditions in step S7

/>

S8-2-4, using step S8-2-3, the following inequality holds:

this means

S8-2-5, under zero initial value, get

Further, the processing unit is used for processing the data,

Thus, the first and second substrates are bonded together,

Thus, the network failure detection system is randomly stable and has a hybrid L ₁ gain performance.

S8-3, the sensitivity of the event triggering filter to the fault detection system is verified.

S8-3-1, the condition for designing the stable operation of the network fault detection system is as follows:

the design constant a >0 is chosen, Λ>0,β_f>0,σ>0,ι₁>0,ι₂>0,κ₁>0,κ₂>0，/>Vector/> And/>Vector quantitySo that

/>

α≥nσ,

For any μ=1, 2, …, n and v=1, 2, …, q, then the network failure detection system is positive, randomly stable and meets the L _- gain performance under the event triggered filter in step S5, where,AndThe gain matrix satisfies

S8-3-2, the verification event triggering filter is sensitive to faults, and comprises positive verification of a network fault detection system and verification of random stability of the network fault detection system, wherein the verification method is the same as that of the step S8-1 and the step S8-2.

Specifically, the positive verification process of the network fault detection system is as follows:

by the extended fault detection system in step S5 and step S8-1-1, for any non-negative initial conditions, we get And/>Wherein,

C_il＝(E_flZ₁C_i C_fl D_fl-C_w),E_il＝E_flZ₁F_i-D_w.

According to the conditions in step S8-3-1, it can be given thatThus,/>Furthermore, A _il is Metzer and/>Thus, the network failure detection system is positive.

Further, the random stability verification process of the network fault detection system is as follows:

The Lyapunov function in step S8-2-1 is selected to obtain AndWherein the method comprises the steps of

/>

Then the first time period of the first time period,

The conditions in the combination step S8-3-1 are as follows

The following inequality is obtained:

this means

Applying Dynkin formula to the above inequality gives

Thus, the first and second substrates are bonded together,

Then the first time period of the first time period,Thus, the network failure detection system is sensitive to failures. /(I)

Claims (11)

1. The self-adaptive event triggering fault detection method of the network system is characterized by comprising the following steps of:

s1, establishing a nonlinear positive half Markov system state space model of a network control system

S1-1, establishing a state space model of a network control system

Wherein,System state, system input and system output, respectively; /(I)Representing an additional disturbance located in L ₁ [0, +#); /(I)Is a fault signal to be detected in L ₁ [0, ]; g _a(x(t))＝(g_a1(x₁(t)),...,g_an(x_n(t)))^- and/>Is a non-linearity of the system; g _b (u (t)) is defined as g _b (w (t)), the system matrix is denoted by A _i,B_i,C_i,D_i,E_i,F_i, where i εS;

S1-2, converting into nonlinear positive semi-Markov system state space model

In probability spaceThe semi-Markov process { r _t, t.gtoreq.0 } defined above is a right-hand continuous process and is performed on a finite set S= {1,2,..For values i not equal to j and q _ii =0, let/>Is a homogeneous Markov update process, where t _k represents the kth jump instant, { X _k } is the associated state in the Markov chain, transition probability q _ij＝P_r{X_k+1＝j|X_k＝i},P_r represents probability, and the time interval between two consecutive jumps τ _k＝t_k-t_k-1 is the dwell time of the semi-Markov process { r _t}_t≥0, where h.gtoreq.0 and/>By calculation, there is/>Lambda _ij (h) is the transfer rate corresponding to the mode j from time t at mode i to time t+delta, and lambda _ij (h) > 0 (i noteqj),/>Let us assume that the transition probability of the semi-markov process r _t satisfies/>

S2, constructing an actuator fault model;

S3, constructing a self-adaptive event triggering strategy;

S4, constructing a new fault signal;

s5, constructing a fault detection filter under the event triggering condition;

s6, constructing a nonlinear function condition;

S7, setting a condition for stable operation of the network fault detection system.

2. The method for detecting an adaptive event-triggered failure of a network system according to claim 1, wherein in step S2, an actuator failure model is constructed as follows:

Wherein, Representing failure modes belonging to a model set: q= {1,2, …, L } and/>Representing the total number of failure modes, a defined diagonal matrix/>Defined as/> Diagonal element/>Is 1 or 0,I is an identity matrix of known dimensions.

3. The method for detecting an adaptive event trigger fault of a network system according to claim 2, wherein in step S3, the adaptive event trigger policy is constructed as follows:

Let t _ι be the iota event trigger time, define the event trigger error function as: Where m (t) is the sampling error,/> The event triggering condition is constructed as follows:

||m(t)||₁＞β(t)||y(t)||₁,

Wherein the adaptive event trigger coefficient β (t) satisfies:

wherein, Λ, beta (0), Are all predefined constants.

4. The method for detecting an adaptive event-triggered failure of a network system according to claim 3, wherein in the step S4, the method for constructing the failure signal is as follows:

The minimum implementation of f _w (t) to estimate the original fault by detecting a new fault signal is given by:

f_w(t)＝C_wg_a(x_w(t))+D_wf(t),

Wherein, Is a weighted failure state,/>Is an original failure,/>Is a weighted failure and a _w,B_w,C_w,D_w is a known matrix.

5. The method for detecting an adaptive event-triggered failure of a network system according to claim 4, wherein the failure detection filter under the event-triggered condition in step S5 is constructed as follows:

Wherein, Is the state vector of the filter,/>Representing residual signal,/>Representing the filter input, defined in probability space/>The upper half Markov process { delta _t, t.gtoreq.0 } is a right continuous process, the finite set of values S= {1,2, …, N },/>And/>Denoted as A _fl,B_fl,C_fl,D_fl,E_fl is the filter matrix to be determined, the relationship between the system pattern r _t and the filter pattern delta _t can be described by a conditional probability matrix Y= { θ _il }, where P _r{δ_t＝l|r_t＝i}＝θ_il, where 0.ltoreq.θ _il.ltoreq.1,/>, for each i.epsilon.S

Definition of the definitionE (t) =r _f(t)-f_w (t), an extended fault detection system is obtained as follows:

Wherein,

Introducing a fault detection mechanism of a residual evaluation function: Where T represents the evaluation time, J _r (T) is the residual evaluation function, and depending on the residual evaluation function selected, the threshold may be defined as: /(I)

Wherein,The fault detection scheme that indicates that all disturbance inputs of L ₁ -norm are in the interval [0, ++), and that determines whether a fault has occurred, can be configured to:

6. the method for detecting an adaptive event-triggered failure of a network system according to claim 5, wherein the nonlinear function condition is constructed in the following manner in step S6:

the nonlinear functions g _a (x (t)) and g _b (x (t)) satisfy the following sector conditions:

wherein 1.ltoreq.i.ltoreq.n, 0 < iota ₁＜ι₂,0＜κ₁＜κ₂ and g _ai(0)＝0,g_bi (0) =0.

7. The method for detecting a failure triggered by an adaptive event in a network system according to claim 6, wherein in step S7, the steady operation condition of the failure detection system is set as follows:

The design constant alpha is more than 0, Λ＞0,γ_w＞0,γ_f＞0,σ＞0,ι₁＞0,ι₂＞0,κ₁＞0,κ₂＞0，/>Vector quantityδ_l＞0,δ_μl＞0,ξ_vl＞0,/>And/>Vector η _l＞0,η_μl＞0,ζ_vl > 0 makes

δ_μl＜δ_l,η_μl＜η_l,α≥nσ,

For any μ=1, 2, …, n and v=1, 2, …, q, the fault detection system is positive, randomly stable and meets the L ₁ gain performance under the event triggered filter in step S4, where,And/>The gain matrix satisfies

8. The method for detecting an adaptive event-triggered failure of a network system according to any one of claims 5 to 7, further comprising step S8 of verifying:

S8-1, positive verification of a fault detection system;

s8-2, verifying random stability of a fault detection system;

s8-3, the sensitivity of the event triggering filter to the fault detection system is verified.

9. The method for detecting a failure triggered by an adaptive event in a network system according to claim 8, wherein in step S8-1, the positive verification method of the failure detection system is as follows:

S8-1-1, consider when in network fault detection system And f (t) =0, using the adaptive event triggering strategy in step S3, one can derive

For any initial condition x (t ₀) > 0, noteThen the first time period of the first time period,

S8-1-2, the extended fault detection system in step S5 and step S8-1-1, for any non-negative initial conditions, result

Wherein,

C_il＝(E_flZ₁C_i C_fl D_fl-C_w),D_il＝(0 E_flZ₁D_i),E_il＝E_flZ₁F_i-D_w.

E _flZ₁F_i-D_w. Gtoreq.0 can be given depending on the conditions in step S7, then E _il. Gtoreq.0, furthermore A _il is Metzer and B _il≥0,C_il≥0,D_il. Gtoreq.0, so the network failure detection system is positive.

10. The method for detecting a failure triggered by an adaptive event in a network system according to claim 9, wherein in step S8-2, the method for verifying the random stability of the failure detection system is as follows:

S8-2-1, the selected Lyapunov function is as follows:

By using the step S8-1-1, it is possible to obtain

Wherein the method comprises the steps of

S8-2-2, thereby obtaining

S8-2-3, in combination with the conditions in step S7

S8-2-4, using step S8-2-3, the following inequality holds:

this means

S8-2-5, under zero initial value, get

And then obtain

Thus (2)

Thus, the fault detection system is randomly stable and has a hybrid L ₁ gain performance.

11. The method for detecting an adaptive event-triggered failure of a network system according to claim 10, wherein: in the step S8-3, the sensitivity verification method of the event triggering filter to the fault detection system is as follows:

S8-3-1, setting a condition for stable operation of the fault detection system, wherein the setting method is the same as that of the step S7;

S8-3-2, the verification event triggering filter is sensitive to faults, and comprises positive verification of a network fault detection system and verification of random stability of the network fault detection system, wherein the verification method is the same as that of the step S8-1 and the step S8-2.