Towards a Global Controller Design for Guaranteed Synchronization of Switched Chaotic Systems

TL;DR

This paper develops a control framework using Lyapunov stability and LMI techniques to ensure guaranteed synchronization of switched chaotic systems, combining robust control and switched system theories.

Contribution

It introduces a novel approach to synchronize switched chaotic systems using bilinear and linear matrix inequalities for controller design.

Findings

Derived a sufficient condition for synchronization using BMIs.

Recast the nonlinear control problem as LMIs for computational efficiency.

Validated the approach with illustrative examples.

Abstract

In this paper, synchronization of identical switched chaotic systems is explored based on Lyapunov theory of guaranteed stability. Concepts from robust control principles and switched linear systems are merged together to derive a sufficient condition for synchronization of identical master-slave switched nonlinear chaotic systems and are expressed in the form of bilinear matrix inequalities (BMIs). The nonlinear controller design problem is then recast in the form of linear matrix inequalities (LMIs) to facilitate numerical computation by standard LMI solvers and is illustrated by appropriate examples.