Stabilization of Semi-Markovian Jumping Uncertain Complex-Valued Networks with Time-Varying Delay: A Sliding-Mode Control Approach

Abstract

This paper pays close attention to the stabilization issue for delayed uncertain semi-Markovian jumping complex-valued networks via sliding mode control. The concerned corresponding transition rates depend on a positive constant, i.e., sojourn-time, which is not required to obey the general exponential distribution. Combine the generalized Dynkin’s formula with Lyapunov stability theory as well as the characteristics of cumulative distribution functions, a few sufficient criteria are proposed to ascertain the stochastic stability of the obtained sliding mode dynamical system. In addition, design a novel sliding mode controller to ensure all state trajectories of the potential closed-loop system can reach the synthesized sliding mode switching surface in a finite time and maintain there in the subsequent time. In the end of paper, one simple example is presented to verify superiority and feasibility of the provided controller design scheme.