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

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 ‐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 ‐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 ‐bound. Finally, the advantages and effectiveness of the proposed methods are demonstrated by three examples.