State-Feedback Filtering for Delayed Discrete-Time Complex-Valued Neural Networks

Delay-dependent Lurie-Postnikov type Lyapunov-Krasovskii functionals for stability analysis of discrete-time delayed neural networks

This paper addresses the influence of time-varying delay and nonlinear activation functions with sector restrictions on the stability of discrete-time neural networks. Compared to previous works that mainly focuses on the influence of delay information, this paper devotes to activation nonlinear functions information to help compensate the analysis technique based on Lyapunov-Krasovskii functional (LKF). A class of delay-dependent Lurie-Postnikov type integral terms involving sector constraints of nonlinear activation function is proposed to complement the LKF construction. The less conservative criteria for the stability analysis of discrete-time delayed networks is given by using improved LKF. Numerical examples show that conservatism can be reduced by the delay-dependent integral terms involving nonlinear activation functions.

Non-fragile output-feedback synchronization for delayed discrete-time complex-valued neural networks with randomly occurring uncertainties

This paper is step forward to establish an exponential synchronization criterion for discrete-time complex-valued neural networks (CVNNs) having time-varying delays subject to randomly occurring uncertain weighting parameters, in order to overcome the fluctuation when the output-feedback controller imposes on its dynamics. To achieve this, Jensen's weighted summation inequalities (WSIs) and an extended reciprocal convex matrix inequality (ERCMI) are extended into the domain of complex field. By introducing some augmented vectors, a Lyapunov-Krasovskii functional (LKF) is constructed to attain an improved delay-dependent linear matrix inequalities (LMIs) constraint for the exponential synchronization phenomenon of the desired master-slave neuronal system model. For instance, the upper bound of the quadratic summation terms occurred in the finite difference of the LKF have been obtained from its linearization that has been made by the developed complex-valued WSIs and complex-valued ERCMI. The proposed results are less restrictive with the minimum number of decision variables than those obtained using existing inequalities. The designed output-feedback control gain has been determined by solving a set of complex-valued LMIs and it has been enforced with a prescribed exponential decay rate. Finally, in sight of MATLAB software, the established results have been examined via a numerical example supported by the simulation results.