Aperiodic Sampled-Data Control for Anti-Synchronization of Chaotic Nonlinear Systems Subject to Input Saturation

Abstract

This paper studies the aperiodic sampled-data (SD) control anti-synchronization issue of chaotic nonlinear systems under the effects of input saturation. At first, to describe the simultaneous existence of the aperiodic SD pattern and the input saturation, a nonlinear closed-loop system model is established. Then, to make the anti-synchronization analysis, a relaxed sampling-interval-dependent Lyapunov functional (RSIDLF) is constructed for the resulting closed-loop system. Thereinto, the positive definiteness requirement of the RSIDLF is abandoned. Due to the indefiniteness of RSIDLF, the discrete-time Lyapunov method (DTLM) then is used to guarantee the local stability of the trivial solutions of the modeled nonlinear system. Furthermore, two convex optimization schemes are proposed to expand the allowable initial area (AIA) and maximize the upper bound of the sampling period (UBSP). Finally, two examples of nonlinear systems are provided to illustrate the superiority of the RSIDLF method over the previous methods in expanding the AIA and enlarging the UBSP.