A fuzzy order reduction filtering method for active memristor systems with FHN characteristics

Abstract

This invention belongs to the field of filter design technology, specifically relating to a fuzzy order reduction filtering method for active memristor systems with FHN characteristics. This invention utilizes a T-S fuzzy model to reconstruct the nonlinear system, establishing multiple simple linear relationships through membership functions to represent complex nonlinear relationships. Then, a novel event-triggered mechanism is employed to improve the utilization rate of the transmission channel. Finally, the unknown parameters of the T-S fuzzy order reduction filter are obtained by solving several linear matrix inequalities. This filter can then be used to filter and control active memristor systems with FHN characteristics. When designing a T-S fuzzy order reduction filter on a distributed parameter system, the system and filtering states are not only time-dependent but also spatially dependent, making it more suitable for practical production needs. Furthermore, the event-triggered mechanism is incorporated into the design process, determining whether a signal should be transmitted based on triggering conditions, effectively improving the utilization efficiency of communication resources.

Description

Technical Field

[0001] This invention belongs to the field of filter design technology, specifically relating to a fuzzy order reduction filtering method for an active memristor system with FHN characteristics. Background Technology

[0002] Over the past few decades, network-based filter design has gained increasing prominence in industrial processes due to its advantages such as ease of installation, flexibility, reliability, and low cost. Although significant theoretical advancements have been achieved in stability analysis and filter design for network systems, many difficulties and prominent problems remain in nonlinear network systems. Therefore, research on filtering problems in nonlinear network systems is of great significance and has broad practical application prospects.

[0003] Traditional communication mechanisms typically employ time-triggered mechanisms. However, in real-world production and daily life, not all sampled data and measurement outputs need to be transmitted. Therefore, this mechanism easily leads to wasted network resources, further exacerbating network latency, data loss, and various other network problems. To overcome this deficiency while ensuring desired system performance, event-triggered communication mechanisms have received widespread attention. Data is only transmitted over the network when a threshold set by the event trigger is met. This effectively reduces data transmission over the network, improves network resource utilization, and aligns with the development trend of engineering research.

[0004] Currently, most modeling is based on lumped parameter systems, which are described by ordinary differential equations (ODEs) and whose states depend only on time. However, for many real-world systems, such as those in thermal, chemical, and aerospace engineering, the state is often determined by both time and space. Therefore, it is crucial to establish systems that adapt to spatiotemporal variations. The inputs and outputs of distributed parameter systems vary not only with time but also with space, often requiring modeling using partial differential equations. Among distributed parameter systems, nonlinear parabolic distributed parameter systems play a vital role in engineering applications and have significant development potential.

[0005] Recently, Luo Jia, Sun Liang, and others proposed a FitzHugh-Nagumo (FHN) neuron model in their paper "An Application of a Novel Active Memristor in Coupled FHN Neural Networks," published in the Journal of Hubei University of Technology in 2020, to characterize memristor synaptic coupling networks such as... Figure 1 As shown, this network exhibits characteristics of a distributed parameter system, often resulting in a high system order, which poses a significant challenge to the subsequent design of the controller / filter. Therefore, methods for simplifying the mathematical model based on reduced-order filters that may emerge under specific conditions are of great importance in practical applications. Summary of the Invention

[0006] This invention provides a fuzzy order reduction filtering method for active memristor systems with FHN characteristics, which can be flexibly applied to practical engineering.

[0007] To solve the above-mentioned technical problems, the technical solutions included in this invention and their corresponding beneficial effects are as follows:

[0008] The present invention provides a fuzzy order reduction filtering method for an active memristor system with FHN characteristics, comprising the following steps:

[0009] 1) Establish an FHN memristor neuron model and represent it as a nonlinear distributed parameter system; based on the set fuzzy rules, linearize the nonlinear distributed parameter system using a TS fuzzy model; the nonlinear distributed parameter system is:

[0010]

[0011] Among them, y t (x,t) represents the partial derivative of the system state with respect to t; Θ represents the coefficient of the reaction diffusion term; y xx (x,t) represents the second partial derivative of the system state with respect to x; y(x,t) represents the system state; f() represents the nonlinear function; c1, c2, d, and e represent constant matrices of appropriate dimensions; ω(x,t) represents external disturbances; z0(x,t) represents the estimated output; z m (x,t) represents the measurement output;

[0012] 2) Based on the set fuzzy filtering rules, determine the TS fuzzy order reduction filter model with unknown parameters; taking into account the sampler, zero-order hold and event triggering mechanism, obtain the input signal of the TS fuzzy order reduction filter, and determine the filter residual model accordingly.

[0013] 3) Construct the Lyapunov function. To ensure the residual system has asymptotic stability under H∞ disturbance rejection decay performance, in Ψ i satisfy In the case of , the unknown parameters in the TS fuzzy reduction filter are solved to obtain the TS fuzzy reduction filter model;

[0014] 4) Using the obtained TS fuzzy reduced-order filter model, filter control is performed on the active memristor system with FHN characteristics.

[0015] The beneficial effects of the above technical solution are as follows: This invention utilizes the Takagi-Sugeno (TS) fuzzy model to reconstruct the nonlinear system, and establishes multiple simple linear relationships through membership function partitioning to represent complex nonlinear relationships; then, a novel event-triggered mechanism is adopted to improve the utilization rate of the transmission channel; finally, the unknown parameters of the TS fuzzy reduction filter are obtained by solving several linear matrix inequalities; and after the TS fuzzy reduction filter is designed, it can be used to filter and control an active memristor system with FHN characteristics. When designing the TS fuzzy reduction filter on a distributed parameter system, the system and filtering state are not only time-dependent but also spatially dependent, making it more suitable for actual production needs and beneficial for engineering practice; moreover, the event-triggered mechanism is incorporated into the design of the TS fuzzy reduction filter, determining whether the signal should be transmitted based on the triggering conditions, effectively improving the utilization efficiency of communication resources.

[0016] Furthermore, in step 1), the FHN memristor neuron model is as follows:

[0017]

[0018]

[0019] Among them, y 1t (x,t) represents the partial derivative of system state 1 with respect to t; y 1xx (x,t) represents the second partial derivative of system state 1 with respect to x; y1(x,t) represents system state 1; y2(x,t) represents system state 2; ω(x,t) represents external disturbance; y 2t (x,t) represents the partial derivative of system state 2 with respect to t; y 2xx (x,t) represents the second partial derivative of system state 2 with respect to x.

[0020] Furthermore, in step 1), the fuzzy rule is: if θ k (x,t) is k = 1, 2, ..., z, where z is a positive integer, then we have:

[0021]

[0022] Among them, θ(x,t)=[θ1(x,t),θ2(x,t),…,θ z [x,t] represents the premise variable; Let A be a fuzzy set, i∈{1,2,…,r}; i C 1i C 2i D i and E i Given a matrix of appropriate dimension;

[0023] The corresponding TS fuzzy system model is:

[0024]

[0025] in, For any x∈[0,l], l is a natural number, t≥0, we have h i (θ(x,t))≥0 and

[0026] Furthermore, in step 2), the fuzzy filtering rule is: if θ k (x,t) is If k = 1, 2, ..., z, then we have:

[0027]

[0028] in, This indicates the state of the TS fuzzy reduction filter, and κ < n; This is the actual input signal to the filter; A is the estimated signal for z0(x,t); ki B ki and C ki The coefficient matrix of the desired TS fuzzy reduction filter with appropriate dimension; Θ k The reaction diffusion coefficient of the filter system;

[0029] The corresponding TS fuzzy order reduction filter model with unknown parameters is as follows:

[0030]

[0031] Furthermore, in step 2), the input signal of the TS fuzzy order reduction filter is obtained through the event triggering mechanism as follows:

[0032]

[0033] Among them, z m (x,t k T) represents the latest transmitted signal; t k Indicates the triggering time; Ω represents a positive definite matrix; ε∈[0,1).

[0034] Furthermore, in step 2), the filter residual model is:

[0035]

[0036] in, col[] represents a column vector; Let represent the augmented system coefficient matrix of the original system and the filtered system, and r < n and both are positive integers.

[0037] Furthermore, in step 3), the constructed Lyapunov function is:

[0038]

[0039]

[0040]

[0041]

[0042]

[0043] Where P, S, Q, and T1 are positive definite matrices, and P 11 ,P 22 Q1, Q3, T 11 ,T 22 P is a positive definite matrix. 12 Q2,T 12 Let be a matrix of any suitable dimension, and * denote the transpose of the diagonal matrix; η(x,s) is an auxiliary state to facilitate integration over t; η s (x,s) is the partial derivative of η(x,s) with respect to s; h represents the upper bound of the network delay obtained by the event trigger, i.e., 0 < h(t) < h.

[0044] Furthermore, in step 3), to ensure the residual system possesses asymptotic stability under H∞ disturbance rejection attenuation performance, combining Schur's complement lemma and Jensen's inequality, we can obtain:

[0045]

[0046] in, The derivative of the Lyapunov function V(t) is expressed as follows; γ > 0 indicates H ∞ Performance index, defined as ξ(x,t)=col[η t (x,t)η(x,t)η x (x,t)η(x,th(t))η(x,th)e k [(x,th(t))ω(x,t)],h i (θ)=h i (θ(x,t)).

[0047] Furthermore, in step 3), the unknown parameters in the TS fuzzy reduction filter are obtained by solving linear matrix inequalities.

[0048] Furthermore, the unknown parameters in the TS fuzzy order reduction filter are:

[0049]

[0050] Among them, A ki B ki C ki Indicates the unknown parameters in the TS fuzzy order reduction filter; and Let represent the parameters obtained by solving linear matrix inequalities, respectively. Further solve for the unknown parameters in the TS fuzzy order reduction filter, i∈{1,2,…,r}. Attached Figure Description

[0051] Figure 1 This is a circuit diagram of a partially active memristor in the prior art;

[0052] Figure 2 This is a flowchart of the fuzzy order reduction filtering method for an active memristor system with FHN characteristics according to the present invention;

[0053] Figure 3 The residual system of this invention The trajectory diagram;

[0054] Figure 4 The residual system of this invention The trajectory diagram;

[0055] Figure 5 This is a schematic diagram illustrating the data transmission time and interval based on event-triggered conditions according to the present invention;

[0056] Figure 6 The reduced-order fuzzy filter H of this invention ∞ Performance diagram. Detailed Implementation

[0057] This invention focuses on the design of an event-triggered reliable H∞ order reduction filter for an active memristor system with FHN characteristics. The entire process is as follows: First, the nonlinear system is reconstructed using a Takagi-Sugeno (TS) fuzzy model, and multiple simple linear relationships are established through fuzzy partitioning of membership functions to represent complex nonlinear relationships. Then, a novel event-triggered mechanism is employed to improve the utilization of the transmission channel. Finally, the unknown parameters of the TS fuzzy order reduction filter are obtained by solving several linear matrix inequalities. After designing the TS fuzzy order reduction filter, it can be used to filter and control an active memristor system with FHN characteristics.

[0058] The following detailed description, in conjunction with the accompanying drawings and embodiments, provides a fuzzy order reduction filtering method for an active memristor system with FHN characteristics according to the present invention.

[0059] Method Implementation Examples:

[0060] An embodiment of the fuzzy order reduction filtering method for an active memristor system with FHN characteristics according to the present invention is as follows: Figure 2 As shown, the entire process is as follows:

[0061] Step 1, based on as follows Figure 1 The circuit diagram of the locally active memristor shown is used to establish an FHN memristor neuron model, which is then represented by a distributed parameter system. Based on the set TS fuzzy rules, the nonlinear distributed parameter system is reconstructed. Specifically:

[0062] 1) Establish the FHN memristor neuron model. The FHN memristor neuron model can be represented as:

[0063]

[0064] Among them, y 1t (x,t) represents the partial derivative of system state 1 with respect to t; y 1xx (x,t) represents the second partial derivative of system state 1 with respect to x; y1(x,t) represents system state 1; y2(x,t) represents system state 2; ω(x,t) represents external disturbance; y 2t (x,t) represents the partial derivative of system state 2 with respect to t; y 2xx (x,t) represents the second partial derivative of system state 2 with respect to x.

[0065] 2) The model in equation (1) can be summarized into a class of nonlinear distributed parameter system models, as shown in equation (2) below:

[0066]

[0067] Among them, y t(x,t) represents the partial derivative of the system state with respect to t; Θ represents the coefficient of the reaction diffusion term; y xx (x,t) represents the second partial derivative of the system state with respect to x; y(x,t) represents the system state; ω(x,t) represents the external disturbance; z0(x,t) represents the estimated output; z m (x,t) represents the measurement output; f() represents the nonlinear function; c1, c2, d, e represent constant matrices with appropriate dimensions.

[0068] 3) Set TS fuzzy rules to linearize the nonlinear parts of the system.

[0069] TS fuzzy rules set For: If θ1(x,t) is θ2(x,t) is ..., θ k (x,t) is Therefore:

[0070]

[0071] Among them, θ(x,t)=[θ1(x,t),θ2(x,t),…,θ z [x,t] represents the premise variable; Let A be a fuzzy set, i∈{1,2,…,r}; k=1,2,…,z, where z is a positive integer; i C 1i C 2i D i and E i Given a matrix of appropriate dimension.

[0072] Therefore, the TS fuzzy system model can be represented as:

[0073]

[0074] in, For any x∈[0,l] (l is a natural number) and t≥0, we have h i (θ(x,t))≥0 and

[0075] Step two: Based on the set fuzzy filtering rules, determine the TS fuzzy order reduction filter model with unknown parameters. Specifically:

[0076] Setting fuzzy filtering rules For: If θ1(x,t) is θ2(x,t) is ..., θ z (x,t) is Therefore:

[0077]

[0078] in, Θ represents the partial derivative of the filter state with respect to t; k Represents the coefficient of the filter reaction diffusion term; This represents the second partial derivative of the filter state with respect to x; This is the actual input signal to the filter; The estimated signal for z0(x,t); This indicates the state of the TS fuzzy reduction filter, and κ < n; Represents κ-dimensional Euclidean space; A ki B ki and C ki It is a coefficient matrix with appropriate dimensions.

[0079] Therefore, the TS fuzzy order reduction filter model can be expressed as:

[0080]

[0081] Step three involves employing a novel event-triggered mechanism to improve network resource utilization efficiency. By incorporating the sampler, zero-order hold, and event-triggered mechanism, the input signal of the TS fuzzy order reduction filter can be obtained, and the filter residual model can be determined accordingly. Specifically:

[0082] 1) In a network, using a sampler and a zero-order hold, the current sampled signal z is transmitted when the threshold condition is met as follows. m (x,t k T+nT):

[0083]

[0084] Among them, z m (x,t k T+nT) represents the current sampled signal; z m (x,t k T) represents the latest transmitted signal; ε∈[0,1); Ω represents a positive definite symmetric matrix; t k The trigger time.

[0085] 2) Considering the event triggering mechanism, the above TS fuzzy system model can be converted into a new system model with time delay.

[0086] Define network time delay as: h(t) = t - (t k T+nT)=ti k T, 0≤h(t)≤h, t∈Λ n,k h(t) represents a time-delay network; ik =t k T+nT represents the current time t. k T to the imminent moment t k+1 The sampling time between T; n is a natural number sequence.

[0087] Therefore, the new event triggering mechanism is described as follows:

[0088]

[0089] Among them, e k (x,i k T)=z m (x,i k T)-z m (x,t k T) represents the transmission error; z m (x,t k T) represents the latest transmitted signal.

[0090] 3) Considering the influence of the zero-order hold, the input signal of the TS fuzzy order reduction filter with unknown parameters can be expressed by the following formula:

[0091]

[0092] Among them, t k+1 =t k +n+1,τ tk τ represents the time delay at the current moment. tk+1 This indicates a time lag in indicating an imminent moment.

[0093] 4) Based on the design method of the reduced-order filter for the event-triggered fuzzy distributed parameter system mentioned above, the following filter residual model is established:

[0094]

[0095] in, col[] represents a column vector; Let represent the augmented system coefficient matrix of the original system and the filtered system, and r < n and both are positive integers.

[0096] Step four: Construct the Lyapunov function. To ensure the residual system possesses asymptotic stability under H∞ disturbance rejection decay performance, while satisfying... In this case, the unknown parameters in the TS fuzzy reduction filter are solved to obtain the TS fuzzy reduction filter model. Specifically:

[0097] 1) Construct the Lyapunov function:

[0098]

[0099] in:

[0100]

[0101]

[0102]

[0103]

[0104] Where P, S, Q, and T1 are positive definite matrices, and P 11 ,P 22 Q1, Q3, T 11 ,T 22 P is a positive definite matrix. 12 Q2,T 12 Let be a matrix of any suitable dimension, and * denote the transpose of the diagonal matrix; η(x,s) is an auxiliary state to facilitate integration over t, and can be omitted; η s (x,s) represents the partial derivative of η(x,s) with respect to s, and can be omitted; h represents the upper bound of the network delay obtained by the event trigger, i.e., 0 < h(t) < h.

[0105] 2) By differentiating the Lyapunov function V(t), we can obtain:

[0106]

[0107]

[0108]

[0109]

[0110] Where, η t (x,t) represents η t Take the partial derivative of (x,t) with respect to t.

[0111] 3) Combining Schur's complement lemma and Jensen's inequality, we can obtain the following conclusion:

[0112]

[0113] in, γ > 0 indicates H ∞ For the sake of convenience, the performance metric is defined as ξ(x,t)=col[η t (x,t)η(x,t)η x (x,t)η(x,th(t))η(x,th)e k[(x,th(t))ω(x,t)],h i (θ)=h i (θ(x,t)).

[0114] 4) To ensure the residual system is asymptotically stable under H∞ disturbance rejection, given scalars γ > 0, ε > 0, and h > 0, there must exist a matrix Ω > 0, S satisfying P > 0, Q > 0, T1 > 0, and G make I represents the identity matrix. Given a matrix with appropriate dimensions.

[0115] 5) Furthermore, combining the above proof process, define the matrix. V = S1, in S1∈R n×n S2∈R r×r ,S3∈R r×r ,

[0116] 6) Decouple the above results, that is, decouple Ψ i Multiply by diag{U} on the left and right respectively. T U T To ensure that the residual system involving the reduced-order filter has asymptotic stability under H∞ disturbance rejection attenuation performance, in addition to satisfying the above conditions, the following must be satisfied:

[0117]

[0118] in,

[0119] 7) Solve for the parameters using the Linear Matrix Inequality (LMI) method. and For i∈{1,2,…,r}, the unknown parameters of the TS fuzzy order reduction filter can be further obtained as follows:

[0120] At this point, the design of the TS fuzzy order reduction filter is complete.

[0121] Step 5: Using the obtained TS fuzzy reduced-order filter model, filter control is performed on the active memristor system with FHN characteristics.

[0122] The effectiveness of the method of the present invention is demonstrated below using simulation methods. Specific simulation data are as follows: h=0.1, ε=0.05, γ=0.5, Θ=Θ k =1, D=-0.01I, C2=-0.01I, E=0.2I. The calculation yields: A k1 = -0.0115, A k2 =-0.0090, B k1 = -0.0016, B k2 = -0.0059. The corresponding residual system trajectory diagram, residual system The trajectory diagram, the data transmission time and interval diagram based on event-triggered conditions, and the TS fuzzy reduction fuzzy filter H ∞ Performance diagrams are as follows: Figure 3 , 4 As shown in Figures 5 and 6. From Figure 3 , Figure 4 It is evident from the data that the designed order-reducing filter can effectively filter and control the system; furthermore, from... Figure 5 As can be seen, using an event-triggered mechanism can effectively reduce the number of data transmissions and lower the communication burden. Finally, Figure 6 express The curve under zero initial conditions shows that ζ(t) < 0, satisfying H ∞ performance.

[0123] In summary, the present invention has the following characteristics:

[0124] 1) This invention is mainly applied to the design of TS fuzzy order reduction filters on distributed parameter systems. Its parameters are coupled in time and space, making it more suitable for actual production needs.

[0125] 2) This invention incorporates an event triggering mechanism in the design of the TS fuzzy order reduction filter, which determines whether the signal is flowing based on the triggering conditions, effectively improving the utilization efficiency of resources.

[0126] 3) This invention filters an active memristor system based on the FHN characteristics of a reduced-order fuzzy filter with H∞. ​​The filter can track the system signal well.

Claims

1. An active memristor system fuzzy reduced-order filtering method with FHN characteristics, characterized in that, The method comprises the following steps: 1) establishing an FHN memristor neuron model, and representing the FHN memristor neuron model as a nonlinear distributed parameter system; based on a set fuzzy rule, linearizing the nonlinear distributed parameter system by using a T-S fuzzy model; the nonlinear distributed parameter system is: where y t (x, t) denotes the partial derivative of the system state with respect to t; Θ denotes the reaction-diffusion term coefficient; y xx (x, t) denotes the second partial derivative of the system state with respect to x; y(x, t) denotes the system state; f() denotes a nonlinear function; c1, c2, d, e denote constant matrices of appropriate dimensions; ω(x, t) denotes an external disturbance; z0(x, t) denotes the estimated output; z m (x, t) denotes the measured output; 2) based on a set fuzzy filtering rule, determining a T-S fuzzy reduced-order filter model with unknown parameters; taking a sampler, a zero-order holder and an event-triggering mechanism into account, obtaining an input signal of the T-S fuzzy reduced-order filter, and determining a filter residual error model correspondingly; 3) Construct the Lyapunov function. To ensure the residual system has asymptotic stability under H∞ disturbance rejection decay performance, in Ψ i satisfy In the case of , the unknown parameters in the TS fuzzy reduction filter are solved to obtain the TS fuzzy reduction filter model; 4) using the obtained T-S fuzzy reduced-order filter model, performing filtering control on the active memristor system with FHN characteristics.

2. The active memristor system fuzzy reduced-order filtering method with FHN characteristics according to claim 1, characterized in that, In step 1), the FHN memristor neuron model is: where y 1t (x, t) denotes the first derivative of the system state 1 with respect to t; y 1xx (x, t) denotes the second derivative of the system state 1 with respect to x; y1(x, t) denotes the system state 1 ; y2(x, t) denotes the system state 2; ω(x, t) denotes the external disturbance; y 2t (x, t) denotes the first derivative of the system state 2 with respect to t; y 2xx (x, t) denotes the second derivative of the system state 2 with respect to x.

3. The active memristor system fuzzy reduction filtering method with FHN characteristics according to claim 1, characterized in that, In step 1), the fuzzy rule is: if θ k (x,t) is z is a positive integer, then there is: where θ(x, t) = [θ1(x, t), θ2(x, t),..., θr(x, t)] represents the premise variables; z (x, t) = [θ1(x, t), θ2(x, t),..., θr(x, t)] represents the premise variables; is a fuzzy set, i e {1, 2,..., r}; A i , C 1i , C 2i , D i and E i are known matrices of appropriate dimensions; The corresponding T-S fuzzy system model is: wherein For any x e [0, 1], 1 being a natural number, t > 0, h i (θ(x, t)) > 0 and 4. The active memristor system fuzzy reduction filtering method with FHN characteristics according to claim 1, characterized in that, In step 2), the blurring filter rule is: if θ k (x,t) is Then there is: wherein, represents the state of the T-S fuzzy reduced-order filter and κ < n; is the actual input signal of the filter; is the estimated signal of z0(x, t); A ki , B ki and C ki is the coefficient matrix of the T-S fuzzy reduced-order filter to be solved with appropriate dimensions; Θ k is the reaction-diffusion coefficient of the filtering system; The corresponding T-S fuzzy reduced-order filter model with unknown parameters is:

5. The active memristor system fuzzy reduction filtering method with FHN characteristics according to claim 1, characterized in that, In step 2), the input signal of the T-S fuzzy reduced-order filter obtained through the event-triggering mechanism is: where z m (x,t k T) represents the latest transmitted signal; t k represents the triggering time; ε∈[0,1); Ω represents a positive definite symmetric matrix.

6. The active memristor system fuzzy reduction filtering method with FHN characteristics according to claim 5, characterized in that, In step 2), the filter residual error model is: wherein col[] denotes a column vector; denotes the augmented system coefficient matrix of the original system and the filter system, and r < n and are positive integers.

7. The active memristor system fuzzy reduction filtering method with FHN characteristics according to claim 1, characterized in that, In step 3), the constructed Lyapunov function is: where P, S, Q, T1 are positive definite matrices, and P 11 ,P 22 ,Q1,Q3,T 11 ,T 22 are positive definite matrices, P 12 ,Q2,T 12 are matrices of any suitable dimension, * denotes the transpose of a diagonal matrix; η(x, s) is an auxiliary state, facilitating the integration of t; η s (x, s) is the partial derivative of η(x, s) with respect to s; h denotes an upper bound on the network delay resulting from event triggering, i.e. 0 < h(t) < h.

8. The active memristor system fuzzy reduced-order filtering method with FHN characteristics according to claim 7, characterized in that, In step 3), in order to make the residual error system have H∞ anti-disturbance attenuation performance and asymptotic stability performance, the Schur complement lemma and the Jensen inequality can be combined to obtain: wherein denotes the derivative of the Lyapunov function V(t); γ > 0 denotes H ∞ performance indicator, defined as ξ(x, t) = col[η t (x, t) η(x, t) η x (x, t) η(x, t - h(t)) η(x, t - h) e k (x, t - h(t)) ω(x, t)], h i (θ) = h i (θ(x, t)).

9. The active memristor system fuzzy reduction filtering method with FHN characteristics according to claim 1, characterized in that, In step 3), the unknown parameters in the T-S fuzzy reduced-order filter are solved by using a linear matrix inequality.

10. The active memristor system fuzzy reduction filtering method with FHN characteristics according to claim 9, characterized in that, The unknown parameters in the T-S fuzzy reduced-order filter are: where A ki , B ki , C ki represent unknown parameters in the T-S fuzzy reduced-order filter; and respectively represent parameters obtained by solving a linear matrix inequality, and further solve the unknown parameters in the T-S fuzzy reduced-order filter, i∈{1,2,…,r}.

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