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

• Published in: IET control theory & applications Vol. 13; no. 18; pp. 3174 - 3183
• Main Authors: Che, Zhiyuan, Yu, Haitao, Yang, Chunyu, Zhou, Linna
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 17.12.2019
• Subjects: adaptive control; adaptive ISMC; Brief Paper; closed loop systems; control system synthesis; controller gain; disturbance observer; disturbance observer‐based adaptive integral sliding mode control; input nonlinearity; linear matrix inequalities; nonlinear control systems; observers; passivity analysis; passivity condition; robust control; singular perturbation; singularly perturbed systems; time‐varying systems; uncertain singularly perturbed systems; uncertain systems; variable structure systems; time-varying systems; singularly perturbed systems; singular perturbation; uncertain systems; adaptive ISMC; passivity condition; adaptive control; control system synthesis; disturbance observer-based adaptive integral sliding mode control; controller gain; uncertain singularly perturbed systems; closed loop systems; input nonlinearity; disturbance observer; linear matrix inequalities; nonlinear control systems; robust control; passivity analysis; variable structure systems; observers
• ISSN: 1751-8644; 1751-8652; 1751-8652
• DOI: 10.1049/iet-cta.2019.0643

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 $\varepsilon $ε-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 $\varepsilon $ε-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 $\varepsilon $ε-bound. Finally, the advantages and effectiveness of the proposed methods are demonstrated by three examples.