Adaptive sliding mode control for fuzzy singular systems with time delay and input nonlinearity

Correspondence Mourad Kchaou, Department of Electrical Engineering, College of Engineering, University of Hail, Hail 2440, Saudi Arabia; or Laboratory of Sciences and Techniques of Automatic Control and Computer Engineering, National Engineering School of Sfax, University of Sfax, 3038 Sfax, Tunisia. Email: mouradkchaou@gmail.com Summary This paper addresses the sliding mode control problem for a class of uncertain Takagi-Sugeno fuzzy singular systems with state delay and subject to input nonlinearity. Our purpose is focused on designing an adaptive sliding mode controller for such a complex system. First, a new fuzzy integral-type sliding function is designed. Then, an adaptive sliding mode control scheme is established such that the resulting closed-loop system is insensitive to all admissible uncertainties and satisfies the reaching condition. Moreover, delay-dependent sufficient conditions are derived such that the admissibility and the L2-L∞ performance requirement of the sliding mode dynamics can be guaranteed in the presence of time delays, external disturbances, and sector nonlinearity input. Finally, the validity and applicability of the proposed theory are illustrated by a numerical example.

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