An LMI approach to robust synchronization of a class of chaotic systems with gain variations

This paper presents a novel approach to robust chaos synchronization by linear-state-feedback controller for a class of uncertain chaotic systems with parameters perturbation, different external disturbances and gain variation on both master system and slave system. Based on the Lyapunov stability theory, a sufficient condition is then proposed in Theorem 1. It is shown that chaos synchronization can be achieved at an exponential convergence rate, when synchronization error will be bounded, as a result of noise presence. Applying Schur complement and some matrix manipulation techniques, the results are then transformed into the linear matrix inequality (LMI) form and are presented in Theorem 2. Error bound is minimized through LMI minimization techniques as given in Theorem 3. Finally, the effectiveness of theorems proposed herein is verified demonstrated by the chaotic Murali–Lakshmanan–Chua system.