Synthesis of the Sliding Mode Control Law of Synchronization of Chaotic Systems Basing on Sequential Aggregate of Invariant Manifolds

The sliding mode control (SMC) synthesis procedures are often used to ensure robustness while providing synchronization of chaotic systems. This paper presents a synthesis procedure for law of sliding mode robust control for Sprott's jerk chaotic system using the Synergetic Control Theory (SCT). This procedure provides: (i) the synthesis of a robust control law; (ii) simultaneous solution of classical subtasks of SMC design for a nonlinear systems; (iii) simplification of stability analysis of a closed-loop system; and also (iv) elimination of a control chattering, i.e. switching of the control law sign.