H∞state estimation for memristive neural networks with time-varying delays: The discrete-time case

Observer-Based Dissipativity Control for T-S Fuzzy Neural Networks With Distributed Time-Varying Delays

An observer-based dissipativity control for Takagi-Sugeno (T-S) fuzzy neural networks with distributed time-varying delays is studied in this article. First, the network channel delays are modeled as a distributed delay with its kernel. To make full use of kernels of the distributed delay, a Lyapunov-Krasovskii functional (LKF) is established with the kernel of the distributed delay. It is noted that the novel LKF and delay-dependent reciprocally convex inequality plays an important role in dealing with global asymptotical stability and strict (Q, S,R) - α -dissipativity of the T-S fuzzy delayed model. Through the constructed LKF, a new set of less conservative linear matrix inequality (LMI) conditions is presented to obtain an observer-based controller for the T-S fuzzy delayed model. This proposed observer-based controller ensures that the state of the closed-loop system is globally asymptotically stable and strictly (Q, S,R) - α -dissipative. Finally, the effectiveness of the proposed results is shown in numerical simulations.

Global Exponential Stability of Memristive Neural Networks With Mixed Time-Varying Delays

This article investigates the Lagrange exponential stability and the Lyapunov exponential stability of memristive neural networks with discrete and distributed time-varying delays (DMNNs). By means of inequality techniques, theories of the M-matrix, and the comparison strategy, the Lagrange exponential stability of the underlying DMNNs is considered in the sense of Filippov, and the globally exponentially attractive set is estimated through employing the M-matrix and external input. Especially, when the external input is not concerned, the Lyapunov exponential stability of the corresponding DMNNs is developed immediately in the form of an M-matrix, which contains some published outcomes as special cases. Furthermore, by constructing an M-matrix-based differential system, the Lyapunov exponential stability of the DMNNs is studied, which is less conservative than some existing ones. Finally, three simulation examples are carried out to examine the validness of the theories.

Exponential State Estimation for Memristor-Based Discrete-Time BAM Neural Networks With Additive Delay Components

This paper focuses on the dynamical behavior for a class of memristor-based bidirectional associative memory neural networks (BAMNNs) with additive time-varying delays in discrete-time case. The necessity of the proposed problem is to design a proper state estimator such that the dynamics of the corresponding estimation error is exponentially stable with a prescribed decay rate. By constructing an appropriate Lyapunov-Krasovskii functional (LKF) and utilizing Cauchy-Schwartz-based summation inequality, the delay-dependent sufficient conditions for the existence of the desired estimator are derived in the absence of uncertainties which are further extended to available uncertain parameters of the prescribed memristor-based BAMNNs in terms of linear matrix inequalities (LMIs). By solving the proposed LMI conditions the estimation gain matrices are obtained. Finally, two numerical examples are presented to illustrate the effectiveness of the proposed results.

Exponential State Estimation for Stochastically Disturbed Discrete-Time Memristive Neural Networks: Multiobjective Approach

The state estimation of the discrete-time memristive model is studied in this article. By applying the stochastic analysis technique, sufficient formulas are established to ensure the exponentially mean-square stability of the error model. Moreover, the derived control gain matrix can be calculated via the linear matrix inequality (LMI). It should be mentioned that, by extending the derived conclusion to a multiobjective optimization problem, the maximum bound of the active function and the minimum bound of the disturbance attenuation are derived. The corresponding simulation figures are provided in the end.

Event-triggered synchronization of discrete-time neural networks: A switching approach

This paper investigates the event-triggered synchronization control of discrete-time neural networks. The main highlights are threefold: (1) a new event-triggered mechanism (ETM) is presented, which can be regarded as a switching between the discrete-time periodic sampled-data control and a continuous ETM; (2) a saturating controller which is equipped with two switching gains is designed to match the switching property of the proposed ETM; (3) a dedicated switching Lyapunov-Krasovskii functional is constructed, which takes the sawtooth constraints of control input into account. Based on these ingredients, the synchronization criteria are derived such that the considered error systems are locally stable. Whereafter, two co-design problems are discussed to maximize the set of admissible initial conditions and the triggering threshold, respectively. Finally, the effectiveness and advantages of the proposed method are validated by two numerical examples.

Delay-Distribution-Dependent H∞ State Estimation for Discrete-Time Memristive Neural Networks With Mixed Time-Delays and Fading Measurements

This paper addresses the H _∞ state estimation issue for a sort of memristive neural networks in the discrete-time setting under randomly occurring mixed time-delays and fading measurements. The main purpose of the addressed issue is to propose a state estimator design algorithm that ensures the error dynamics of the state estimation to be stochastically stable with a prespecified H _∞ disturbance attenuation index. We put forward certain switching functions to account for the discrete-time yet state-dependent characteristics of the memristive connection weights. By resorting to the robust analysis theory and the Lyapunov-functional analysis theory, we derive some sufficient conditions to guarantee the desired estimation performance. The derived sufficient conditions rely not only on the size of discrete time-delays and the probability distribution law of the distributed time-delays but also on the statistics information of the coefficients of the adopted Rice fading model. Based on the established existence conditions, the gain matrices of the desired estimator are obtained by means of the feasibility of a set of matrix inequalities that can be checked efficiently via available software packages. Finally, the numerical simulation results are provided to show the validity of the main results.

Finite-time nonfragile time-varying proportional retarded synchronization for Markovian Inertial Memristive NNs with reaction-diffusion items

The issue of synchronization for a class of inertial memristive neural networks over a finite-time interval is investigated in this paper. Specifically, reaction-diffusion items and Markovian jump parameters are both considered in the system model, meanwhile, a novel nonfragile time-varying proportional retarded control strategy is proposed. First, a befitting variable substitution is invoked to transform the original second-order differential system into a first-order one so that the corresponding synchronization error system that is represented by a first-order differential form is established. Second, by utilizing the integral inequality technique, reciprocally convex combination approach and free-weighting matrix method, a less conservative synchronization criterion in terms of linear matrix inequalities is obtained. Finally, three simulations are exploited to illustrate the feasibility, practicability and superiority of the designed controller so that the acquired theoretical results are supported.

Non-fragile state estimation for fractional-order delayed memristive BAM neural networks

This paper deals with the non-fragile state estimation problem for a class of fractional-order memristive BAM neural networks (FMBAMNNs) with and without time delays for the first time. By means of a novel transformation and interval matrix approach, non-fragile estimators are designed and parameter mismatch problem is averted. Sufficient criteria are established to ascertain the error system is asymptotically stable based on fractional-order Lyapunov functionals and linear matrix inequalities (LMIs). Two examples are put forward to show the effectiveness of the obtained results.

Reduced-Order Filtering of Delayed Static Neural Networks With Markovian Jumping Parameters

The reduced-order filtering problems are investigated in this paper for static neural networks with Markovian jumping parameters and mode-dependent time-varying delays. By fully making use of integral inequalities, the designs of reduced-order and filters are discussed. The proper gain matrices of filters and the optimal performance indices are efficiently obtained by resolving corresponding convex optimization problems with the constraints of linear matrix inequalities. It is verified that the computational complexity for the reduced-order filter design is significantly reduced when compared with the full-order one. Furthermore, the nonfragile reduced-order filtering problems are also resolved in this paper. Two examples with simulation results are presented to demonstrate the feasibility and application of the established results.

Dissipativity-Based Resilient Filtering of Periodic Markovian Jump Neural Networks With Quantized Measurements

The problem of dissipativity-based resilient filtering for discrete-time periodic Markov jump neural networks in the presence of quantized measurements is investigated in this paper. Due to the limited capacities of network medium, a logarithmic quantizer is applied to the underlying systems. Considering the fact that the filter is realized through a network, randomly occurring parameter uncertainties of the filter are modeled by two mode-dependent Bernoulli processes. By establishing the mode-dependent periodic Lyapunov function, sufficient conditions are given to ensure the stability and dissipativity of the filtering error system. The filter parameters are derived via solving a set of linear matrix inequalities. The merits and validity of the proposed design techniques are verified by a simulation example.