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This article proposes a time‐varying nonsingular terminal sliding mode (TSM) control for a class of uncertain second‐order nonlinear system and its application to n‐links rigid robotic manipulators. First, a time‐varying nonsingular terminal sliding manifold is developed by incorporating a piecewise‐defined function of time into a nonsingular TSM manifold. As a result, the singularity problem is avoided and the reaching phase existing in conventional TSM control is totally suppressed which ensures the global robustness of the system against uncertainties and disturbances. Moreover, adaptive tuning laws are developed to omit the requirement of prior knowledge of the upper bound of the lumped uncertainty. In particular, an effective method is provided for the parameters selection to meet a prespecified convergence time. Hence, the convergence time to the origin of the tracking errors can be specified in advance according to the mission requirements. The formulation of the controllers and the stability analysis are verified by Lyapunov theory. Simulation results and comparative studies are presented to demonstrate the effectiveness and the superiority of the proposed algorithms. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 (𝓆𝒮ℛ)‐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. [ABSTRACT FROM AUTHOR]

SUMMARY This 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. [ABSTRACT FROM AUTHOR]