LMI synchronization conditions for variable fractional-order one-sided Lipschitz chaotic systems with gain fluctuations

Abstract

This article addresses the synchronization of general variable fractional-order one-sided Lipschitz chaotic systems with norm-bounded time-varying parametric uncertainty. A non-fragile state feedback control scheme is designed to cope with uncertainties in the controller gain fluctuations, and a sufficient condition for master/slave synchronization and determination of the controller gain is derived and expressed as a linear matrix inequality. The new control approach is applicable to fractional-order Lipschitz chaotic systems as well as to integer-order systems. Additionally, compared with other existing schemes, the method is easier and less costly to implement in real-world applications. Three numerical examples are given to show the performance of the non-fragile control approach for synchronizing practical chaotic systems.