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Summary: This article deals with the problem of robust output feedback control design for a class of switched systems with uncertainties and random time‐varying delay. Our purpose is focused on designing a full order dynamic output feedback controller and an appropriate switching rule to ensure the exponential mean square stability of the resulting closed‐loop switching system with an l2−l∞ performance level. The appealing aspects of the proposed control scheme include: (a) the development of LMI based delay‐dependent sufficient conditions for the exponential stability analysis of the stochastic hybrid systems using the appropriate choice of the augmented Lyapunov–Krasovskii functional, the partitioning technique and the average dwell time, (b) conservatism reduction of the unified design conditions, and (c) the controller designed exhibiting robustness with l2−l∞ performance against uncertainties and external disturbance. Finally, representative examples are given to demonstrate the validity and the merit of the proposed design technique. [ABSTRACT FROM AUTHOR]

This study deals with (Q,S,R) ‐ γ ‐dissipative output feedback control design for a class of switched systems with time‐varying delay and unmeasurable states. The purpose is to design an observer‐based controller and a switching rule to ensure both exponential stability and strict dissipativity of the resulting closed‐loop switched systems. Using an augmented switched Lyapunov–Krasovskii functional with triple sum and the improved reciprocally convex combination approach, new sufficient conditions are developed in terms of linear matrix inequalities. Simulation examples are included to demonstrate the validity and effectiveness of the proposed design technique. [ABSTRACT FROM AUTHOR]

Summary: This paper investigates the problem of control design for a class of uncertain switched singular systems with time‐varying delay. Under mode‐dependent average dwell time and using an appropriate Lyapunov‐Krasovskii functional, the exponential admissibility of the system is analyzed. In order to obtain less conservative conditions, the delay partitioning technique is adopted as well as the improved reciprocally convex approach. By means of the developed admissibility condition, a static output feedback controller is then designed using linear matrix inequality approach. Moreover, by solving an optimization convex problem with constraints, the switched controller is developed to ensure simultaneously the stability of the closed‐loop system and satisfy an optimized upper bound of both the linear quadratic guaranteed cost and the H∞ norm. Numerical examples are proposed to verify the efficiency and the merits of the method proposed. [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]

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]

SUMMARY This paper presents a new approach for delay-dependent H∞ stability analysis and control synthesis for singular systems with delay. By constructing an augmented Lyapunov-Krasovskii functional with a triple-integral term, and using the partitioning technique, a bounded real lemma is presented to ensure the singular state-delay system to be regular, impulse free and stable with γ-disturbance rejection. The proposed result leads to significant performance improvement in system analysis and synthesis. Based on the criterion obtained, a homotopy-based iterative LMI algorithm is developed to design a static output feedback controller. The feasibility and the effectiveness of theoretical developments are illustrated through numerical examples.Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY In this paper, the problem of delay-dependent robust L2 − L ∞ (energy to peak) control for a class of uncertain fuzzy descriptor systems with time-varying delay is investigated. The parametric uncertainties are assumed to be of a linear fractional form involving all system matrices. First, a delay-dependent criterion is given in terms of LMIs to guarantee that the fuzzy descriptor system is regular, impulse free, and stable. Based on this criterion, a state fuzzy feedback controller is designed to ensure that the closed-loop system is regular, impulse free, and robustly stable with a prescribed L2 − L ∞ performance satisfied for all admissible parameter uncertainties. Numerical examples are given to show the effectiveness of the proposed approach. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We present a new family of ninth‐order hybrid explicit Numerov‐type methods, effectively utilizing only eight stages, for solving the special second‐order initial value problem. After applying a number of simplifying assumptions, we arrive to a reduced set of order conditions. Then, we derive an optimal method with constant coefficients that requires one less stage than standard methods found in the literature that use nine stages at this moment. Numerical tests are conducted using quadruple precision arithmetic on several well‐known problems and the superiority of the new method is clear. Finally, in Section 6, a Mathematica package is presented that implements the corresponding algorithm. [ABSTRACT FROM AUTHOR]