A method for detecting memory faults in a randomly occurring saturated uncertain networked system

Abstract

The present invention discloses a memory fault detection method for an uncertain networked system under random saturation, the method comprising the following steps: step 1, establishing an uncertain networked system model with random sensor saturation; step 2, designing a memory-based fault detection filter and obtaining a residual dynamic system; step 3, based on Finsler's lemma, obtaining a residual system that is finite-time stable and satisfies H ∞ The judgment basis of performance index constraint; Step 4, solve the fault detection filter gain matrix by the judgment basis and matrix inequality method; Step 5, substitute the filter gain matrix into the fault detection filter to obtain the residual; Step 6, construct a fault detection mechanism with residual evaluation function and threshold, and judge whether the fault occurs by calculating the residual evaluation function and threshold. This method can reduce the impact of saturation and uncertainty on the performance of the fault detection filter and detect the occurrence of faults more quickly.

Description

Technical Field

[0001] The invention relates to a network system fault detection method, in particular to a finite time memory fault detection method for an uncertain network system under random sensor saturation. Background Art

[0002] The purpose of fault detection is to issue an alarm in time for potential fault signals in the system to prevent the occurrence of faults that may lead to system performance degradation and avoid unnecessary economic losses and casualties. With the development of computer technology and network communication technology, networked systems have emerged and are constantly developing in a larger and more complex direction. This trend has led to higher and higher requirements for the security and reliability of networked systems, so it is more important to develop more effective fault detection technology.

[0003] Due to physical or technical limitations, many unreliable communication phenomena may occur in networked systems, and sensor saturation is one of them. The occurrence of saturation is random, which will cause the remote filter to be unable to receive complete measurement information. On the other hand, system modeling often has deviations, that is, the model has parameter uncertainty. If the randomly occurring sensor saturation phenomenon and parameter uncertainty cannot be effectively handled, this will reduce the performance of the fault detection algorithm to a certain extent. Therefore, it is of practical value to study the fault detection method of uncertain networked systems under random saturation.

[0004] In addition, in the current fault detection method design process, only one-step filter state and measurement information are usually used, which will increase the conservatism of the fault detection method and reduce the fault detection performance. Therefore, it is necessary to develop a new memory fault detection method that fully utilizes the filter / measurement information in a limited time when constructing the filter. Summary of the invention

[0005] In order to better handle the fault detection problem of networked systems with random sensor saturation and parameter uncertainty, the present invention provides a memory fault detection method for uncertain networked systems under random saturation. The method constructs a memory fault detection filter based on the historical state information of the filter, which can detect the occurrence of faults more quickly.

[0006] The objective of the present invention is achieved through the following technical solutions:

[0007] A method for detecting memory faults in an uncertain networked system under random saturation conditions comprises the following steps:

[0008] Step 1: Establish an uncertain networked system model with randomly occurring sensor saturation:

[0009] x(k+1)=(A+α(k)ΔA)x(k)+h(x(k))+Dω(k)+Gf(k),

[0010] y(k)=β(k)σ(Cx(k))+(1-β(k))Cx(k)+Ev(k),

[0011]

[0012] Wherein, k represents the time, and k∈[0,N], N is a positive integer; x(k) represents the system state at time k; x(k+1) represents the system state at time k+1; y(k) represents the measured output of the system at time k; h(·) represents a nonlinear function; ω(k) and v(k) both represent external disturbances at time k; f(k) represents the fault signal to be detected at time k; σ(·) is the sensor saturation function; A, D, G, C and E are constant matrices of appropriate dimensions; ΔA represents parameter uncertainty; α(k), β(k) are Bernoulli random variables; x(0) represents the initial state of the system; Indicates the value of the initial state;

[0013] Step 2: Design a memory-based fault detection filter and obtain the residual dynamic system. The specific steps are as follows:

[0014] Step 21: Construct a memory fault detection filter of the following form:

[0015]

[0016]

[0017]

[0018] Where h is the memory window domain, h<N; x F (ki) represents the state vector of the fault detection filter at time ki; x F (k+1) represents the state vector of the fault detection filter at time k+1; r(k) is the residual signal of the filter at time k; B F , D F , are the memory fault detection filter parameters to be designed; i = 0, 1, 2, ..., h-1;

[0019] Step 2: In order to improve the performance of fault detection, consider weighted fault f w (k) = W(k)f(k), where W(k) represents the prior weighting matrix, and the weighting system is expressed as follows:

[0020] x w (k+1)=A w xw (k)+B w f(k),

[0021] f w (k) = C w x w (k)+D w f(k),

[0022] Among them, x w (k) is the state vector of the weighted system at time k; x w (k+1) is the state vector of the weighted system at time k+1; A w , B w , C w and D w is a pre-selected constant matrix;

[0023] Step 23: Define the state augmentation vector at time k State augmentation vector at time k+1 k-time perturbation augmented vector The residual error signal at time k is e(k) = r(k) - f w (k), according to the uncertain networked system model in step 1, the memory fault detection filter in step 21 and the weighted system in step 22, the following residual system is obtained:

[0024]

[0025]

[0026] Where:

[0027]

[0028]

[0029]

[0030]

[0031]

[0032]

[0033] Where 0 and I represent the zero matrix and the identity matrix with appropriate dimensions, respectively;

[0034] Step 24: In order to realize the design of memory fault detection filter, rewrite the residual system in a time-invariant way and define the time-invariant state augmented vector η(k) = [ξ T (k-h+1) … ξ T(k-1) ξ T (k)] T , the time-invariant state augmentation vector η(k+1) = [ξ T (k-h+2) … ξ T (k) ξ T (k+1)] T , and obtain the new residual system:

[0035]

[0036]

[0037] In the formula,

[0038]

[0039]

[0040]

[0041]

[0042] Step 3: Based on Finsler's lemma, the residual system is finite-time stable and satisfies H ∞ The basis for determining performance indicator constraints:

[0043] Θ+He{KT}<0,

[0044]

[0045] In the formula,

[0046]

[0047] Ψ=Ψ1+Ψ2,

[0048]

[0049]

[0050] He{A} means A+A T ,λ max (·) represents the maximum eigenvalue of the matrix “·”, λ min (·) represents the minimum eigenvalue of the matrix “·”; γ, χ, c1, c2 represent scalars and satisfy γ>0, χ>1, c2>c1≥0;

[0051] Step 4: Solve the fault detection filter gain matrix using the judgment basis in step 3 and the matrix inequality method. The specific steps are as follows:

[0052] Transform the judgment basis Θ+He{KT}<0 in step 3 to obtain the matrix inequality Combination Solve for the positive scalar ε, the positive definite matrix P, and appropriate dimension matrix The fault detection filter gain matrix is ​​obtained

[0053] Where:

[0054]

[0055] K i1 =[K i11 K i12 ], K i2 =[K i21 K i22 ](i=1,2,3),

[0056]

[0057]

[0058]

[0059]

[0060]

[0061]

[0062]

[0063]

[0064]

[0065]

[0066]

[0067]

[0068]

[0069] in, is a pre-given matrix, K i11 , K i21 and is a suitable-dimensional matrix;

[0070] Step 5: Substitute the filter gain matrix B obtained in step 4 F , D F , and Substitute into the fault detection filter in step 2 to obtain the residual r(k) at time k;

[0071] Step 6: Construct a fault detection mechanism with a residual evaluation function and a threshold. By calculating the residual evaluation function and the threshold, determine whether a fault occurs. The specific steps are as follows:

[0072] Step 6.1: In order to realize system fault detection, construct and calculate the residual evaluation function J k and the detection threshold J th :

[0073]

[0074] In the formula, J k represents the residual evaluation function, J th represents the threshold; sup(*) represents the supremum;

[0075] Step 62: Detect whether the discrete networked system has a fault according to the following judgment criteria:

[0076]

[0077] Compared with the prior art, the present invention has the following advantages:

[0078] 1. The present invention proposes a fault detection method for an uncertain networked system under random saturation, which can reduce the impact of saturation and uncertainty on the performance of the fault detection filter.

[0079] 2. The present invention designs a memory-based fault detection filter, which utilizes the historical status information of the fault detection filter to solve the problem of insufficient utilization of filter data. Compared with the traditional memoryless fault detection method that only considers the state of one-step filter, it can detect the occurrence of faults more quickly and has a better fault detection effect.

[0080] 3. The present invention uses Finsler's lemma to analyze and derive the residual system that satisfies finite-time stability and specifies H ∞ Sufficient conditions for performance constraints are given, and a specific design method for the filter gain matrix is ​​given. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 It is a flow chart of the finite-time memory fault detection method for uncertain networked systems under randomly occurring sensor saturation.

[0082] Figure 2It is the residual graph obtained by the memory-based fault detection method of the present invention, where “—” is the trajectory of the residual r(k).

[0083] Figure 3 It is the residual evaluation function and threshold diagram obtained by the memory-based fault detection method of the present invention, wherein “––” represents the threshold value and “-” represents the residual evaluation function.

[0084] Figure 4 It is the residual graph obtained by the memoryless fault detection method, where “-” is the trajectory of the residual r(k).

[0085] Figure 5 is the residual evaluation function and threshold diagram obtained by the memoryless fault detection method, where “––” represents the threshold and “-” represents the residual evaluation function. DETAILED DESCRIPTION

[0086] The technical solution of the present invention is further described below in conjunction with the accompanying drawings, but is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention should be included in the protection scope of the present invention.

[0087] The present invention provides a method for detecting memory faults in an uncertain networked system under random saturation. Figure 1 As shown, the method comprises the following steps:

[0088] Step 1: Establish an uncertain networked system model with randomly occurring sensor saturation:

[0089]

[0090] In the formula, k represents the time, and k∈[0,N], N is a positive integer; represents the system state vector at time k, represents n-dimensional Euclidean space; represents the system state vector at time k+1; represents the measured output at time k, Represents n y Vieux-style space; represents a nonlinear function; and Both represent the external disturbance at time k, represents the fault signal to be detected at time k, represents n1, n2, n f dimensional Euclidean space; σ(·) is the sensor saturation function; A, D, G, C and E are constant matrices of appropriate dimensions, ΔA represents parameter uncertainty; x(0) represents the initial state of the system; Indicates the value of the initial state;

[0091] The uncertainty ΔA of the system parameters should satisfy the following constraints:

[0092] ΔA=HFM (2)

[0093] Among them, H, M are known dimension constant matrices, and F is the matrix that satisfies the constraint condition F T The unknown matrix F ≤ I, where I represents the identity matrix of appropriate dimensions and T represents the transpose.

[0094] Assuming a nonlinear function Satisfies h(0)=0, and for have:

[0095] [h(θ1)-h(θ2)-Λ1(θ1-θ2)] T [h(θ1)-h(θ2)-Λ2(θ1-θ2)]≤0, (3)

[0096] Among them, Λ1 and Λ2 are known constant matrices and Λ1>Λ2. Let θ1=x(k), θ2=0, we can get:

[0097]

[0098] In the formula,

[0099]

[0100] The saturation function σ(·) has the following form:

[0101]

[0102] Among them, σ i (μ i )=sign(μ i )min{μ i,max ,|μ i |}(i=1,2,,n y ), is a symbolic function, min{*} means taking the minimum value in the set {*}, μ i,max is the saturation vector μ max The i-th element of , |·| means taking the absolute value of “·”.

[0103] Assume that there are two diagonal matrices L1 and L2 (0≤L1<I≤L2) such that σ(Cx(k)) can be decomposed into the following form:

[0104] σ(Cx(k))=σ s (Cx(k))+L1Cx(k) (6)

[0105] In the formula, σs (Cx(k)) is a nonlinear function that satisfies the following conditions:

[0106]

[0107] In the formula, L = L2-L1. In addition, the above inequality can be written as follows:

[0108]

[0109] In the formula,

[0110] Bernoulli random variables α(k) and β(k) describe the randomly occurring parameter uncertainty and sensor saturation, respectively, and have the following statistical properties:

[0111]

[0112]

[0113] Among them, Prob{·} represents the probability of event “·” occurring; E{*} represents the mathematical expectation of random event “*”; is a known constant.

[0114] Step 2: Design a memory-based fault detection filter and obtain the residual dynamic system. The specific steps are as follows:

[0115] Step 21: Construct a memory fault detection filter of the following form:

[0116]

[0117] Where h is the memory window domain (h<N), represents the state vector of the fault detection filter at time ki, represents the state vector of the fault detection filter at time k+1, Represents n F Violette space, is the residual signal of the filter at time k, B F , D F , are the memory fault detection filter parameters to be designed.

[0118] Step 2: In order to improve the performance of fault detection, consider weighted fault f w (k) = W(k)f(k), where W(k) represents the prior weighting matrix. The weighting system can be expressed as follows:

[0119]

[0120] in, is the state vector of the weighted system at time k, is the state vector of the weighted system at time k+1, Represents n w A dimensional space w , B w , C w and D w is a pre-selected constant matrix.

[0121] Step 23: Define the state augmentation vector at time k State augmentation vector at time k+1 k-time perturbation augmented vector The residual error signal at time k is e(k) = r(k) - f w (k), according to the uncertain networked system model (1) in step 1, the memory fault detection filter (9) in step 21 and the weighted system (10) in step 22, the following residual system is obtained:

[0122]

[0123] Where:

[0124]

[0125]

[0126]

[0127]

[0128]

[0129]

[0130] Where 0 and I represent the zero matrix and the identity matrix with appropriate dimensions, respectively;

[0131] Step 24: In order to realize the design of memory fault detection filter, rewrite the residual system in a time-invariant way and define the time-invariant state augmented vector η(k) = [ξ T (k-h+1) … ξ T (k-1) ξ T (k)] T , the time-invariant state augmentation vector η(k+1) = [ξ T (k-h+2) … ξ T (k) ξ T (k+1)] T , and obtain the new residual system:

[0132]

[0133] In the formula,

[0134]

[0135]

[0136]

[0137]

[0138] Step 3: Based on Finsler's lemma, the residual system is finite-time stable and satisfies H ∞ The basis for determining performance indicator constraints:

[0139]

[0140] In the formula,

[0141]

[0142] Ψ=Ψ1+Ψ2,

[0143]

[0144]

[0145] In the formula, He{A} represents A+A T ,λ max (·) represents the maximum eigenvalue of the matrix “·”, λ min (·) represents the minimum eigenvalue of the matrix “·”, γ, χ, c1, c2 represent scalars, and satisfy γ>0, χ>1, c2>c1≥0.

[0146] In this step, the finite time stability and H ∞ The performance is defined as follows:

[0147] (1) When When the matrix R>0, the scalars c1 and c2 satisfy the constraint c2≥c1≥0, if the following equation holds:

[0148]

[0149] Then the residual system is finite-time stable.

[0150] (2) When When , under zero initial conditions, given a scalar γ>0, if e(k) satisfies the following constraints:

[0151]

[0152] Then the residual system satisfies H ∞ Performance indicator constraints.

[0153] Step 4: Solve the fault detection filter gain matrix using the judgment basis in step 3 and the matrix inequality method. The specific steps are as follows:

[0154] Transform the judgment basis Θ+He{KT}<0 in step 3 to obtain the matrix inequality Combination Solve for the positive scalar ε, the positive definite matrix P, and appropriate dimension matrix The fault detection filter gain matrix is ​​obtained

[0155] Where:

[0156]

[0157] K i1 =[K i11 K i12 ], K i2 =[K i21 K i22 ](i=1,2,3),

[0158]

[0159]

[0160]

[0161]

[0162]

[0163]

[0164]

[0165]

[0166]

[0167]

[0168]

[0169]

[0170]

[0171] in, is a pre-given matrix, K i11 , K i21 (i=1, 2, 3) and is a suitable-dimensional matrix.

[0172] Step 5: Substitute the filter gain matrix obtained in step 4 into the fault detection filter in step 2 to obtain the residual. The specific steps are as follows:

[0173] The filter gain matrix B obtained in step 4 F , D F , and Substitute into the fault detection filter in step 2 to obtain the residual r(k) at time k;

[0174] Step 6: Construct a fault detection mechanism with a residual evaluation function and a threshold. By calculating the residual evaluation function and the threshold, determine whether a fault occurs. The specific steps are as follows:

[0175] Step 6.1: In order to realize system fault detection, construct and calculate the residual evaluation function J k and the detection threshold J th :

[0176]

[0177] In the formula, J k represents the residual evaluation function, J th represents the threshold; sup(*) represents the supremum;

[0178] Step 62: Detect whether the discrete networked system has a fault according to the following judgment criteria:

[0179]

[0180] Example:

[0181] This embodiment uses the method of the present invention to conduct the following simulation experiment on an uncertain networked system under random saturation:

[0182] The matrix parameters of uncertain networked systems under random saturation are: The parameters associated with parameter uncertainty are: M = [0.02 -0.04], The relevant parameters of the nonlinear function are:

[0183] The relevant parameters for randomly occurring sensor saturation are: μ i,max =0.5, The relevant parameters of the weighted system are: A w =0.5, B w =0.25, C w =0.15, D w =0.1. Design auxiliary matrix The initial values ​​of other relevant parameters are: R=I, c1=0.5, c2=2.8, χ=1.03, N=25, γ=4.2.

[0184] In order to verify the effectiveness of the memory fault detection filter model designed by the present invention, it is assumed that the external disturbances are ω(k)=0.4sin(0.1k)u(k), v(k)=0.4cos(0.1k)u(k), u(k), u(k) represents the noise uniformly distributed in the interval [-0.5, 0.5], and the fault signal is: sin(·) represents a sine function.

[0185] Case 1: When using a memory-based fault detection filter, assuming h = 2, after calculation, the memory fault detection filter parameter matrix is ​​obtained as:

[0186]

[0187] D F =[0.1649 0.1495];

[0188] Given the initial state of the system Under the influence of external disturbance, the residual error and residual evaluation function generated by the memory fault detection filter are compared with the threshold value as follows: Figure 2 and Figure 3 As shown. When a fault occurs, the memory fault detection filter can quickly detect the fault. From (16), the threshold J th =0.01298, and J(8)<J th <J(9), indicating that the fault can be detected after 1 step.

[0189] Case 2: When using a traditional memoryless fault detection filter, that is, h = 1, after calculation, the fault detection filter parameter matrix is ​​obtained as:

[0190]

[0191] C F =[0.0024 0.0024], D F =[-0.0002 0.0012];

[0192] Given the same initial state The residual error and residual evaluation function generated by the memoryless fault detection filter are as follows: Figure 4 and Figure 5 As shown. From (16), we can get the threshold J th =0.00036 and J(9)<J th <J(10), indicating that the fault can be detected 2 steps after it occurs. Through this embodiment, it can be found that the memory-based fault detection scheme can detect the fault 1 step in advance. Compared with the traditional memory-free fault detection scheme, the present invention can improve the fault detection efficiency by 50%.

Claims

1. A method for detecting memory faults in uncertain networked systems under random saturation, characterized in that The method comprises the following steps: Step 1: Establish an uncertain networked system model with randomly occurring sensor saturation: x(k+1)=(A+α(k)ΔA)x(k)+h(x(k))+Dω(k)+Gf(k), y(k)=β(k)σ(Cx(k))+(1-β(k))Cx(k)+Ev(k), Wherein, k represents the time, and k∈[0,N], N is a positive integer; x(k) represents the system state at time k; x(k+1) represents the system state at time k+1; y(k) represents the measured output of the system at time k; h(·) represents a nonlinear function; ω(k) and v(k) both represent external disturbances at time k; f(k) represents the fault signal to be detected at time k; σ(·) is the sensor saturation function; A, D, G, C and E are constant matrices of appropriate dimensions; ΔA represents parameter uncertainty; α(k), β(k) are Bernoulli random variables; x(0) represents the initial state of the system; Indicates the value of the initial state; Step 2: Design a memory-based fault detection filter and obtain the residual dynamic system. The specific steps are as follows: Step 21: Construct a memory fault detection filter of the following form: Where h is the memory window domain, h<N; x F (ki) represents the state vector of the fault detection filter at time ki; x F (k+1) represents the state vector of the fault detection filter at time k+1; r(k) is the residual signal of the filter at time k; B F , D F , are the memory fault detection filter parameters to be designed; i = 0, 1, 2, ..., h-1; Step 2: In order to improve the performance of fault detection, consider weighted fault f w (k) = W(k)f(k), where W(k) represents the prior weighting matrix, and the weighting system is expressed as follows: x w (k+1)=A w x w (k)+B w f(k), f w (k)=C w x w (k)+D w f(k), Among them, x w (k) is the state vector of the weighted system at time k; x w (k+1) is the state vector of the weighted system at time k+1; A w , B w , C w and D w is a pre-selected constant matrix; Step 23: Define the state augmentation vector at time k State augmentation vector at time k+1 k-time perturbation augmented vector The residual error signal at time k is e(k) = r(k) - f w (k), according to the uncertain networked system model in step 1, the memory fault detection filter in step 21 and the weighted system in step 22, the following residual system is obtained: Where: Where 0 and I represent the zero matrix and the identity matrix with appropriate dimensions, H and M are known constant matrices of appropriate dimensions, and F is the matrix that satisfies the constraint condition F. T Unknown matrix F≤I; Step 24: Define the invariant state augmentation vector η(k) = [ξ T (k-h+1)…ξ T (k-1)ξ T (k)] T , the time-invariant state augmentation vector η(k+1) = [ξ T (k-h+2)…ξ T (k)ξ T (k+1)] T , and obtain the new residual system: In the formula, Step 3: Based on Finsler's lemma, the residual system is finite-time stable and satisfies H ∞ The basis for determining performance indicator constraints: Θ+He{KT}<0, In the formula, Ψ=Ψ1+Ψ2, He{A} means A+A T ,λ max (·) represents the maximum eigenvalue of the matrix "·", λ min (·) represents the minimum eigenvalue of the matrix "·"; γ, χ, c1, c2 represent scalars and satisfy γ>0, χ>1, c2>c1≥0; P represents a positive definite matrix; Step 4: Solve the fault detection filter gain matrix using the judgment basis in step 3 and the matrix inequality method. The specific steps are as follows: Transform the judgment basis Θ+He{KT}<0 in step 3 to obtain the matrix inequality Combination Solve for the positive scalar ε, the positive definite matrix P, and appropriate dimension matrix The fault detection filter gain matrix is ​​obtained Where: Z=[εZ1Z2 T ], K i1 =[K i11 K i12 ],K i2 =[K i21 K i22 ](i=1,2,3), in, is a pre-given matrix, K i11 , K i21 and is a suitable-dimensional matrix; Step 5: Substitute the filter gain matrix B obtained in step 4 F , D F , and Substitute into the fault detection filter in step 2 to obtain the residual r(k) at time k; Step 6: Construct a fault detection mechanism with a residual evaluation function and a threshold. By calculating the residual evaluation function and the threshold, determine whether a fault occurs. The specific steps are as follows: Step 6.1: In order to realize system fault detection, construct and calculate the residual evaluation function J k and the detection threshold J th : In the formula, J k represents the residual evaluation function, J th represents the threshold; sup(*) represents the supremum; Step 62: Detect whether the discrete networked system has a fault according to the following judgment criteria:

2. The method for detecting memory faults in uncertain networked systems under random occurrence saturation according to claim 1 is characterized in that In step 1, ΔA satisfies the following constraints: ΔA=HFM.

3. The method for detecting memory faults in uncertain networked systems under random occurrence saturation according to claim 1 is characterized in that In step 1, it is assumed that the nonlinear function h(·) satisfies h(0)=0, and for have: [h(θ1)-h(θ2)-Λ1(θ1-θ2)] T [h(θ1)-h(θ2)-Λ2(θ1-θ2)]≤0, Among them, Λ1 and Λ2 are known constant matrices and Λ1>Λ2, let θ1=x(k), θ2=0, we get: In the formula, 4. The method for detecting memory faults in uncertain networked systems under random occurrence saturation according to claim 1 is characterized in that In step 1, the saturation function σ(·) has the following form: Among them, σ i (μ i )=sign(μ i )min{μ i,max ,|μ i |}(i=1,2,…,n y ), is a symbolic function, min{*} means taking the minimum value in the set {*}, μ i,max is the saturation vector μ max The i-th element of , |·| means taking the absolute value of "·".

5. The method for detecting memory faults in uncertain networked systems under random occurrence saturation according to claim 1 is characterized in that In the step 1, it is assumed that there are two diagonal matrices L1 and L2, 0≤L1<I≤L2, so that σ(Cx(k)) is decomposed into the following form: σ(Cx(k))=σ s (Cx(k))+L1Cx(k), In the formula, σ s (Cx(k)) is a nonlinear function that satisfies the following conditions: Where L = L2-L1, the above inequality can be written as follows: In the formula, 6. The method for detecting memory faults in uncertain networked systems under random occurrence saturation according to claim 1 is characterized in that In step 1, α(k) and β(k) respectively describe the randomly occurring parameter uncertainty and sensor saturation, and have the following statistical characteristics: Among them, Prob{·} represents the probability of event "·" occurring; E{*} represents the mathematical expectation of random event "*"; is a known constant.

7. The method for detecting memory faults in uncertain networked systems under random occurrence saturation according to claim 1 is characterized in that In step 3, the finite time stability and H ∞ The performance is defined as follows: (1) When When the matrix R>0, the scalars c1 and c2 satisfy the constraint c2≥c1≥0, if the following equation holds: Then the residual system is finite-time stable; (2) When When , under zero initial conditions, given a scalar γ>0, if e(k) satisfies the following constraints: Then the residual system satisfies H ∞ Performance indicator constraints.

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