Title: Modified single phase sliding mode control for a class of mismatched uncertain systems

Authors: Viet Anh Duong

Addresses: Department of Applied Engineering and Technology, University of Science and Technology of Hanoi, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet Street, Cau Giay District, Hanoi 100000, Vietnam

Abstract: This paper presents a new sliding mode control (SMC) concept for guaranteeing the invariance of a linear time varying uncertain system to mismatched uncertainties over all time. Two sets of exponential-type switching surfaces are proposed to eliminate the effect of the mismatched uncertainties in the sliding mode. By nature of these surfaces, the reaching phase is eliminated to avoid the non-robustness associated with that phase, at the same time, the system states are always confined to the new sliding mode from the initial time. Moreover, necessary and sufficient invariance conditions are given such that mismatched uncertainties completely vanish from the entire response of the system at the very beginning time. A linear matrix inequalities (LMIs)-based design method for the switching surfaces is also given. In addition, a control law is constructed to maintain the sliding mode. Finally, numerical results are presented to demonstrate the effectiveness of the proposed concept.

Keywords: invariance condition; SMC; sliding mode control; matched and mismatched uncertainty; LMIs; linear matrix inequalities; invariance property.

DOI: 10.1504/IJAAC.2025.144723

International Journal of Automation and Control, 2025 Vol.19 No.2, pp.164 - 187

Accepted: 19 Apr 2024
Published online: 28 Feb 2025 *

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