Passivity analysis and disturbance observer‐based adaptive integral sliding mode control for uncertain singularly perturbed systems with input non‐linearity

Abstract

This study addresses the problems of passivity analysis and disturbance observer-based adaptive integral sliding mode control (ISMC) for uncertain singularly perturbed systems (SPSs) with input non-linearity. Firstly, the passivity condition enabling system exponentially stable is presented in terms of linear matrix inequalities (LMIs). Secondly, a singular perturbation parameter e-dependent disturbance observer is constructed, and the estimate is incorporated in the design of the adaptive ISMC with the reachability condition guaranteed. Then, a set of LMIs are obtained to determine the controller gain of the ISMC, and an e-bound estimation approach is derived, such that the closed-loop SPSs are passive and exponentially stable. Compared with the existing results, the proposed approaches have less conservatism because of adopting a more general storage function, which leads to a superior transient performance and a bigger e-bound. Finally, the advantages and effectiveness of the proposed methods are demonstrated by three examples.