Adaptive sliding mode control of uncertain chaotic systems with input nonlinearity

This paper is concerned with the stabilization problem of uncertain chaotic systems with input nonlinearity. The slope parameters of this nonlinearity are unmeasured. A new sliding function is designed, then an adaptive sliding mode controller is established such that the trajectory of the system converges to the sliding surface in a finite time and finite-time reachability is theoretically proved. Using a virtual state feedback control technique, sufficient condition for the asymptotic stability of sliding mode dynamics is derived via linear matrix inequality (LMI). Then the results can be extended to uncertain chaotic systems with disturbances and adaptive sliding mode H _∞ controllers are designed. Finally, a simulation example is presented to show the validity and advantage of the proposed method.