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This paper investigates the controller design problem for mean-square asymptotical synchronization of discrete-time neural networks with time-varying delay. We proposed the design method of synchronization controller, which considered the nonlinearity of controller input. Based on the designed controller, a delay-dependent synchronization criterion is proposed and formulated in the form of linear matrix inequalities (LMIs) by applying the Lyapunov function method. The result is extended to the delayed discrete-time neural network with uncertainty. Two numerical examples are presented to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The stability and stabilisation problems for a series of continuous stochastic singular systems with multiple time-varying delays are studied in this paper. First, a useful lemma is proposed and a delay-distribution-dependent Lyapunov functional is constructed. Then, a novel delay-distribution-dependent condition is given to ensure the unforced stochastic singular systems to be regular and impulse-free. The mean-square exponential stability of the whole system is guaranteed under the proposed lemma. As a result, a suitable feedback controller is designed via strict linear matrix inequality such that the system's stabilisation problem is guaranteed. Finally, numerical examples are illustrated to show the proposed result are less conservative than the existing ones and the potential of such technology. [ABSTRACT FROM AUTHOR]

In this paper, the mean-square exponential stability problem for discrete-time recurrent neural networks with time-varying discrete and distributed delays is investigated. Considering the delay distributions, a novel class of Lyapunov functional is introduced. By exploiting all possible information in mixed time delays, a sufficient condition for the whole system to be mean-square exponentially stable is given. Numerical examples are proposed to illustrate the effectiveness of the method, and show that by using the approach in this paper, the obtained results are less conservative than the existing ones. [ABSTRACT FROM AUTHOR]

The problem of robust stabilisation for uncertain discrete singular systems with time-varying delay is discussed in this article. First, a new delay-distribution-dependent Lyapunov function is established. Then, sufficient conditions are proposed for guaranteeing that the uncertain discrete singular system with time-varying delay has the properties of regularity, causality and stability. Finally, a suitable robust state feedback controller is designed by linear matrix inequality. Numerical examples illustrate that the results derived from the proposed method are less conservative than the existing ones. [ABSTRACT FROM AUTHOR]

The problem of chattering free sliding mode control for a class of uncertain discrete singular systems with state delay is investigated in this paper. As a component of the solution, a new least squares support vector machine ( LS- SVM) reaching law is proposed. In terms of linear matrix inequalities, a delay-dependent condition for sliding mode dynamics to be regular, causal, and asymptotically stable is established, and the chattering problem that appears in traditional variable structure systems is eliminated. Numerical examples are provided to demonstrate the applicability of the proposed methods. [ABSTRACT FROM AUTHOR]