In this paper, the synchronization problem for delayed continuous time nonlinear complex neural networks is considered. The delay dependent state feed back synchronization gain matrix is obtained by considering more general case of time-varying delay. Using Lyapunov stability theory, the sufficient synchronization criteria are derived in terms of Linear Matrix Inequalities (LMIs). By decomposing the delay interval into multiple equidistant subintervals, Lyapunov-Krasovskii functionals (LKFs) are constructed on these intervals. Employing these LKFs, new delay dependent synchronization criteria are proposed in terms of LMIs for two cases with and without derivative of time-varying delay. Numerical examples are illustrated to show the effectiveness of the proposed method.

The paper is concerned with the state estimation problem for a class of neural networks with Markovian jumping parameters. The neural networks have a finite number of modes and the modes may jump from one to another according to a Markov chain. The main purpose is to estimate the neuron states, through available output measurements such that for all admissible time-delays, the dynamics of the estimation error are globally stable in the mean square. A new type of Markovian jumping matrix P i is introduced in this paper. The discrete delay is assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Based on the new Lyapunov-Krasovskii functional, delay-interval dependent stability criteria are obtained in terms of linear matrix inequalities (LMIs). Finally, numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed LMI conditions.

No abstract

We study generalized variable projective synchronization between two unified time delayed systems with constant and modulated time delays. A novel Krasovskii-Lyapunov functional is constructed and a generalized sufficient condition for synchronization is derived analytically using the Lyapunov stability theory and adaptive techniques. The proposed scheme is valid for a system of n-numbers of first order delay differential equations. Finally, a new neural oscillator is considered as a numerical example to show the effectiveness of the proposed scheme.