Backstepping based stabilization and synchronization of a class of fractional order chaotic systems

This paper presents stabilization and synchronization problem of a class of fractional order chaotic systems. A systematic step by step approach is explained to derive control results using backstepping strategy. The analytically obtained control structure, derived by blending systematic backstepping procedure with Mittag-Leffler stability results, helps in obtaining stability of strict feedback like class of chaotic systems. The results are based on fractional order extension of Lyapunov stability criterion which is a more realistic approach for analysis of stability of fractional order nonlinear systems. These results are further extended to achieve synchronization of these systems in master-slave configuration. Thereafter, the methodology has been applied to two example systems of the same class to show the application of results. Numerical simulation given at the end confirms the efficacy of the scheme presented here.