Robust chaos suppression for the family of nonlinear chaotic systems with noise perturbation

This paper investigates the robust chaos suppression problem for some classical Rossler systems using the sliding mode controller (SMC). Based on the proportional-integral (PI) switching surface, a SMC is derived to not only guarantee asymptotical stability of the equilibrium points of the Rossler systems but also reduce the effect of noise perturbation to an H-infinity-norm performance. The parameter matrix necessary for constructing both PI switching surface and the SMC can be easily solved by the linear matrix inequality (LMI) optimization technique. Finally, two illustrative examples are provided to demonstrate the efficacy of the proposed control methodology. (C) 2007 Elsevier Ltd. All rights reserved.