Control of chaotic systems with disturbances using LMI-based twisting-like algorithm

This paper proposes a chaos control scheme for stabilizing chaotic systems in the presence of external disturbances. The scheme is based on a twisting-like algorithm, which consists of a state feedback control law and the twisting algorithm (TA). The TA is one of the promising high-order sliding-mode control algorithms. The Lyapunov direct method is utilized to derive a sufficient stability condition. The condition is formulated in a Linear Matrix Inequality (LMI) form and therefore is readily solved. The Lorenz system with an external disturbance is used as a demonstrative example. Numerical results illustrate the effectiveness of the proposed control scheme.