Adaptive variable structure control for uncertain chaotic systems containing dead-zone nonlinearity

This paper addresses a practical tracking problem for a class of uncertain chaotic systems with dead-zone nonlinearity in the input function. Based on the Lyapunov stability theorem and Barbalat lemma, an adaptive variable structure controller (AVSC) is proposed to ensure the occurrence of the sliding mode even though the control input contains a dead-zone. Also it is worthy of note that the proposed AVSC involves no information of the upper bound of uncertainty. Thus, the limitation of knowing the bound of uncertainty in advance is certainly released. Furthermore, in the sliding mode, the investigated uncertain chaotic system remains insensitive to the uncertainty, and behaves like a linear system. Finally, a well-known Duffing–Holmes chaotic system is used to demonstrate the feasibility of the proposed AVSC.