This article is devoted to solving the exponential synchronization problem of a new type of fuzzy memristive neural network with reaction-diffusion terms. By introducing adaptive laws, two controllers are designed. After combining the inequality technique with the Lyapunov function approach, some easily verified sufficient conditions are established to ensure the exponential synchronization of the reaction-diffusion fuzzy memristive system under the proposed adaptive scheme. In addition, by using the Hardy-Poincarè inequality, the diffusion terms are estimated associated with the information of the reaction-diffusion coefficients and the regional feature, which improves some existing conclusions. Finally, an illustrative example is presented to demonstrate the validity of the theoretical results.

In this article, we consider exponential estimation and passivity of memristive neural networks with quaternion parameters. A Takagi–Sugeno type rule is introduced into the quaternion memristive neural networks, which makes the system much easier. To achieve the exponential stability of the estimation error system, a proper controller is designed, which derived in the two norm form. Further, the quasi-state estimation condition is also considered. Along with Lyapunov theory, some criteria are obtained to achieve the exponential passivity of the discussed system.

In this article, the problem of passivity and dissipativity analysis is investigated for a class of fractional-order quaternion-valued fuzzy memristive neural networks. Based on the famous nonlinear scalarizing function, a nonlinear scalarization method is developed, which can be employed to compare the "size" of two different quaternions. In this way, the convex closure proposed by the quaternion-valued connection weights is meaningful. By constructing proper Lyapunov functional, several improved passivity criteria and dissipativity conclusions are established, which can be checked efficiently by utilizing some standard mathematical calculations. Finally, the obtained results are validated by simulation examples.

This article presents the theoretical results on the$H_\infty $state estimation problem for a class of discrete-time memristive neural networks. By utilizing a Lyapunov–Krasovskii functional, sufficient conditions are derived to guarantee that the error system is exponentially mean-square stable; subsequently, the prespecified$H_\infty $disturbance rejection attenuation level is also guaranteed. It should be noted that the vector optimization method is employed to find the maximum bound of function and the minimum disturbance turning simultaneously. Finally, the corresponding simulation results are included to show the effectiveness of the proposed methodology.

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.

This paper is concerned with the finite-time stochastically stability (FTSS) analysis of Markovian jump memristive neural networks with partly unknown transition probabilities. In the neural networks, there exist a group of modes determined by Markov chain, and thus, the Markovian jump was taken into consideration and the concept of FTSS is first introduced for the memristive model. By introducing a Markov switching Lyapunov functional and stochastic analysis theory, an FTSS test procedure is proposed, from which we can conclude that the settling time function is a stochastic variable and its expectation is finite. The system under consideration is quite general since it contains completely known and completely unknown transition probabilities as two special cases. More importantly, a nonlinear measure method was introduced to verify the uniqueness of the equilibrium point; compared with the fixed point Theorem that has been widely used in the existing results, this method is more easy to implement. Besides, the delay interval was divided into four subintervals, which make full use of the information of the subsystems upper bounds of the time-varying delays. Finally, the effectiveness and superiority of the proposed method is demonstrated by two simulation examples.

In this paper, the finite-time stability analysis of non-autonomous and autonomous fractional order memristive systems with a pure time delay and commensurate order between 0 and 1 is proposed. First, two appropriate concepts of the finite-time stability for the mentioned system with and without external input are introduced. Then, a sufficient condition for finite-time stability of the underlying system is derived in the frame of some useful inequalities and appropriate properties of the norm. In particular, the results are presented in form of algebraic inequality, which turn out to be more efficient from the computational point of view. Finally, simulation results are given to testify the merits of the derived conditions.