Stabilization of a class of fractional order chaotic systems via backstepping approach

This paper addresses the stabilization problem of a class of fractional order chaotic systems. The analytically obtained control structure, derived by blending the systematic backstepping procedure with Mittag-Leffler and Lyapunov stability results, helps in obtaining stability of a special case of strict feedback class of fractional order chaotic systems and at the same time avoids the singularity problem. The stabilizing controller is derived for a class of three dimensional systems which can be expressed in strict-feedback form. Thereafter, the methodology has been applied to two example systems i.e. chaotic Lorenz system and Lü system belonging to the addressed class to show the application of results. Numerical simulation results given at the end confirm the efficacy of the scheme presented here.