Yijun Zhang

Delay-Distribution-Dependent Stability and Stabilization of T–S Fuzzy Systems With Probabilistic Interval Delay

In this paper, we are concerned with the problem of stability analysis and stabilization control design for Takagi-Sugeno (T-S) fuzzy systems with probabilistic interval delay. By employing the information of probability distribution of the time delay, the original system is transformed into a T-S fuzzy model with stochastic parameter matrices. Based on the new type of T-S fuzzy model, the delay-distribution-dependent criteria for the mean-square exponential stability of the considered systems are derived by using the Lyapunov-Krasovskii functional method, parallel distributed compensation approach, and the convexity of some matrix equations. The solvability of the derived criteria depends not only on the size of the delay but also on the probability distribution of the delay taking values in some intervals. The revisions of the main criteria in this paper can also be used to deal with the case when only the information of variation range of the delay is considered. It is shown by practical examples that our method can lead to very less conservative results than those by other existing methods.

New stability criteria of neural networks with interval time-varying delay: A piecewise delay method

Abstract This paper provides improved conditions for the global asymptotic stability of a class of neural networks with interval time-varying delays. A piecewise delay method is firstly proposed. In this method, the variation interval of the time delay is divided into two subintervals by introducing its central point. Then, by constructing a new Lyapunov–Krasovskii functional and checking its variation in the two subintervals, respectively, some new delay-dependent stability criteria for the addressed neural networks are derived. Numerical examples are provided to show that the achieved conditions are less conservative than some existing ones in the literature.

Robust delay-distribution-dependent stability of discrete-time stochastic neural networks with time-varying delay

A robust delay-distribution-dependent stochastic stability analysis is conducted for a class of discrete-time stochastic delayed neural networks (DSNNs) with parameter uncertainties. The effects of both variation range and distribution probability of the time delay are taken into account in the proposed approach. The distribution probability of time delay is translated into parameter matrices of the transferred DSNNs model, in which the parameter uncertainties are norm-bounded, the stochastic disturbances are described in term of a Brownian motion, and the time-varying delay is characterized by introducing a Bernoulli stochastic variable. Some delay-distribution-dependent criteria for the DSNNs to be robustly globally exponentially stable in the mean square sense are achieved by Lyapunov method and introducing some new analysis techniques. Two numerical examples are provided to show the effectiveness and applicability of the proposed method.

Delay-Distribution-Dependent Exponential Stability Criteria for Discrete-Time Recurrent Neural Networks With Stochastic Delay

This brief is concerned with the analysis problem of global exponential stability in the mean square sense for a class of linear discrete-time recurrent neural networks (DRNNs) with stochastic delay. Different from the prior research works, the effects of both variation range and probability distribution of the time delay are involved in the proposed method. First, a modeling method is proposed by translating the probability distribution of the time delay into parameter matrices of the transformed DRNN model, where the delay is characterized by a stochastic binary distributed variable. Based on the new method, the global exponential stability in the mean square sense for the DRNNs with stochastic delay is investigated by using the Lyapunov-Krasovskii functional and exploiting some new analysis techniques. A numerical example is provided to show the effectiveness and the applicability of the proposed method.

Robust global synchronization of complex networks with neutral-type delayed nodes

In this paper, the problems of robust global exponential synchronization for a class of complex networks with time-varying delayed couplings are considered. Each node in the network is composed of a class of delayed neural networks described by a nonlinear delay differential equation of neutral-type. Since model errors commonly exist in practical applications, the parameter uncertainties are involved in the considered model. Sufficient conditions that ensure the complex networks to be robustly globally exponentially synchronized are obtained by using the Lyapunov functional method and some properties of Kronecker product. An illustrative example is presented to show the effectiveness of the proposed approach.

Network-Based Synchronization of Delayed Neural Networks

This paper focuses on network-based master-slave synchronization for delayed neural networks through a remote controller. The insertion of communication networks in a master-slave synchronization scheme inevitably induces network delays, packet dropouts and stochastic fluctuations. The data packets may be received with a different temporal order from that they are sent due to the fact that the network-induced delay is time-varying. A logic data processor and a logic zero order hold are proposed in the master-slave synchronization framework. Then an error system for the master system and the slave system is formulated. By combining a generalized Jensen integral inequality and a convex combination technique, some synchronization criteria are derived to ensure the mean-square global exponential synchronization of state trajectories for the master system and the slave system. The controller gain matrix is obtained by solving a minimization problem in terms of linear matrix inequalities using a cone complementary technique. As a special case in which only network-induced delays and packet dropouts are occurred in the signal transmission channels, some results are also presented. Finally, two illustrative examples are provided to show the effectiveness and applicability of the proposed scheme.

Global Exponential Adaptive Synchronization of Complex Dynamical Networks With Neutral-Type Neural Network Nodes and Stochastic Disturbances

This paper is on the design problem of global exponential adaptive synchronization for a class of stochastic complex dynamical networks. In the considered networks, the dynamics of each node are approximated by a neutral-type neural network. The stochastic disturbances are described in terms of Brownian motions. Different from the prior references, the coefficient matrix of the adaptive controller under consideration is an arbitrary matrix instead of an identity one. By using Lyapunov method and some properties of Kronecker product, a sufficient condition is proposed to ensure the dynamics of the considered network globally exponentially synchronize with the desired solution in the mean square sense. Some criteria for global exponential adaptive synchronization of complex dynamical networks with general nodes are further provided in forms of corollaries. In particular, the proposed criteria for network synchronization are in terms of linear matrix inequalities. Only two variables are used in each criterion and the variables are not inside of any Kronecker product. Hence, the conditions are easy to check. A numerical example is presented to show the effectiveness and applicability of the proposed approach.

Novel robust stability criteria of discrete-time stochastic recurrent neural networks with time delay

The problem of robust global exponential stability is investigated for a class of stochastic uncertain discrete-time recurrent neural networks with time delay. In this paper, the midpoint of the time delays variation interval is introduced, and the variation interval is divided into two subintervals. Then, by constructing a new Lyapunov-Krasovskii functional and checking its variation in the two subintervals, respectively, some novel delay-dependent stability criteria for the addressed neural networks are derived. Numerical examples are provided to show that the achieved conditions are less conservative than some existing ones in the literature.

On improved delay-dependent robust H∞ control for systems with interval time-varying delay

Abstract This paper considers the design problem of delay-dependent robust H ∞ control for interval time-delay systems (ITDS). Based on the Lyapunov–Krasovskii functional approach and the convexity of the matrix equations, a delay-dependent bounded real lemma (BRL) is firstly proposed, which is shown in terms of linear matrix inequalities. Then by applying the BRL, sufficient conditions can be obtained for the asymptotic stabilizability of the uncertain ITDS with a prescribed H ∞ performance index. Finally, numerical examples are provided to illustrate the less conservativeness of the proposed methods than some existing results.

Letters: Stability analysis of stochastic neural networks with Markovian jump parameters using delay-partitioning approach

In this paper, the problem of mean square asymptotic stability of stochastic neural networks with Markovian jumping parameters is considered. By choosing an augmented Lyapunov-Krasovskii functional and utilizing the delay-partitioning method, novel delay-dependent mean square asymptotic stability conditions are derived in terms of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness of the proposed approach.