A Dissipative Integral Sliding Mode Control Redesign Method

Abstract

This paper develops a new method of integral sliding mode control redesign for a class of perturbed nonlinear dissipative switched systems by modifying the dissipativity-based control law that was designed for the unperturbed systems. The nominal model is considered affine with matched and unmatched perturbations. The redesigned control law includes an integral sliding-based control signal such that the system always operates on the sliding mode and the dissipativity of the perturbed switched system is maintained from the initial time of the system operation for the norm bounded perturbations. The proposed techniques eliminates the restrictive design conditions on the derivative of storage functions offered in a recent work. In addition, the global dissipativity of the perturbed system is always maintained if the original unperturbed system is globally dissipative. Depending on the type of stability of the unperturbed system, the designed control law for the perturbed system guarantees robust exponential or asymptotic stability of the closed-loop system. The theoretical results are applied to nonlinear switched systems, and the convergence of the state vectors to the origin is verified by simulation in presence of nonlinear perturbations.

Keywords

• Nonlinear switched systems
• dissipativity
• perturbation
• integral sliding mode control
• control redesign.