Controlling hyperchaotic Rabinovich system with single state controllers: Comparison of linear feedback, sliding mode, and passive control methods

Abstract

In this study, the control of hyperchaotic Rabinovich system is applied by using three different single state controllers, namely linear feedback, sliding mode, and passive control. Routh–Hurwitz criterions are used for constructing the sufficient conditions of the linear feedback controller. An appropriate switching surface is designed based on the sliding mode control theory. In order to ensure the global asymptotic stability of the system with the passive controller, a Lyapunov function is used. Simulation results are demonstrated not only to validate all the theoretical analyses but also to compare the effectiveness of proposed control methods. By adding the controllers to the hyperchaotic Rabinovich system, it asymptotically stabilizes towards its zero equilibrium point in the state space. Numerical simulations have also shown that the proposed single state sliding mode controller is more effective than linear feedback and passive controllers on the control of hyperchaotic Rabinovich system.