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SUMMARYThe issue of exponential stability analysis of continuous‐time switched singular systems consisting of a family of stable and unstable subsystems with time‐varying delay is investigated in this paper. It is very difficult to analyze the stability of such systems because of the existence of time‐delay and unstable subsystems. In this regard, on the basis of the free‐weighting matrix approach, by constructing the new Lyapunov‐like Krasovskii functional, and using the average dwell‐time approach, delay‐dependent sufficient conditions are derived and formulated in terms of LMIs to check the exponential stability of such systems. This paper also highlights the relationship between the average dwell‐time of the switched singular time‐delay system, its stability, exponential convergence rate of differential states, and algebraic states. Finally, a numerical example is given to confirm the analytical results and illustrate the effectiveness of the proposed strategy. Copyright © 2012 John Wiley & Sons, Ltd.

Summary In this work, the problem of stability analysis for a class of singular hybrid switched and impulsive system (HSIS) is addressed. Corresponding to each subsystem, a hybrid switched and impulsive controller is designed and then the exponential stability property of the proposed singular HSIS is discussed for linear and nonlinear cases. Because switched systems without impulses are a special case of HSISs, the results are also given to switched system with synchronous and asynchronous controllers. The obtained results apply to control singular systems, and the introduced theorems allow knowing how the control must be designed. Two numerical examples are given to show the effectiveness of the proposed approaches. At first, by using MATLAB® software, the proposed method is applied to a class of physiological processes of endocrine disruptor diethylstilbestrol models to illustrate the effectiveness of the results obtained here for the linear case. Thereafter, another numerical example is provided to support the presented theoretical results for the nonlinear case.

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