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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 L 2 -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. KEYWORDSadaptive sliding mode control, fuzzy singular systems, LMI, time delay 464

The problem of sliding-mode control (SMC) with dissipativity for a class of time-delay Takagi-Sugeno fuzzy singular systems is investigated. The system is subject to uncertainties and input non-linearity. Based on an integral sliding surface, a delay-dependent criterion is developed in terms of linear matrix inequalities, which ensures the sliding mode dynamics to be robustly admissible and strictly (Q, S, R)-dissipative. Moreover, an SMC law is established such that the reachability of the specified sliding surface is guaranteed. Finally, the validity and applicability of the proposed approach are illuminated by two simulation examples.

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SUMMARYThis paper is concerned with the stability analysis and robust dynamic output feedback controller synthesis for uncertain continuous singular systems with time‐delay. First, on the basis of the Lyapunov functional method and by resorting to the delay‐partition technique, improved delay‐dependent sufficient conditions are presented to ensure the nominal unforced system to be admissible (i.e., to be regular, impulse‐free, and stable). Second, with the help of the obtained admissibility criterion, an observer‐based controller is designed by solving a set of LMIs. Finally, the validity and applicability of the proposed approach is shown by examples. Copyright © 2013 John Wiley & Sons, Ltd.