Stability Properties of Switched Singular Systems Subject to Impulsive Effects

Mohamad S. Alwan (), Humeyra Kiyak () and Xinzhi Liu ()
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Mohamad S. Alwan: University of Waterloo, Department of Applied Mathematics
Humeyra Kiyak: University of Waterloo, Department of Applied Mathematics
Xinzhi Liu: University of Waterloo, Department of Applied Mathematics

A chapter in Mathematical and Computational Approaches in Advancing Modern Science and Engineering, 2016, pp 355-365 from Springer

Abstract: Abstract This paper addresses impulsive switched singular systems Impulsive switched singular systems with nonlinear perturbation term. The main theme is to establish exponential stability Exponential stability of the systems where the impulses are of fixed time type and treated as perturbation. We first establish the exponential stability of a single-mode impulsive systems using the Lyapunov method Lyapunov method . We have observed that if the underlying continuous system is stable and the impulses are applied slowly, then it is guaranteed that the impulsive system maintains the stability property. Later, a switched system with impulsive effects is considered. The method of multiple Lyapunov function Multiple Lyapunov functions and average dwell time Average dwell time switching signal are used. We have noticed that if all subsystems are exponentially stable and the average dwell time is sufficiently large, then the impulsive switched system is exponentially stable. Numerical examples with simulations are given to illustrate the effectiveness of the proposed theoretical results.

Keywords: Singular Systems; Impulsive Events; Average Dwell Time Switching Signal; Multiple Lyapunov Functions; Impulsive Systems (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-30379-6_33

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DOI: 10.1007/978-3-319-30379-6_33

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