Controlling chaotic systems with disturbance using backstepping design and nonlinear damping

In this paper the attention is focused on the control of chaotic systems in the presence of unknown and bounded disturbance added to the control input. The issue is tackled by exploiting backstepping design and nonlinear damping. In particular, backstepping is proposed as a systematic Lyapunov-based tool for controlling a large class of chaotic systems, whereas nonlinear damping is suggested to counteract the disturbance affecting the control input. Finally, the effectiveness of the proposed approach is illustrated by stabilizing the chaotic dynamics of the Lorenz system in the presence of a disturbance matched with the control input.