Existence of Solutions and Finite-Time Stability for Nonlinear Singular Discrete-Time Neural Networks

Abstract

This paper investigates the problem of finite-time stability and control for a class of nonlinear singular discrete-time neural networks with time-varying delays and disturbances. First, based on the implicit function theorem and singular value decomposition method, a sufficient condition for the existence of the solution of such systems is established in terms of a linear matrix inequality (LMI). Then, using the Lyapunov functional approach combined with LMI technique we provide new delay-dependent sufficient conditions for robust $$H_{\infty }$$ finite-time stability and control. Finally, some numerical examples are given to illustrate the efficiency of the proposed results.