On singular hybrid switched and impulsive systems

Abstract

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.