Switched Singularly Perturbed Systems with Reliable Controllers

Mohamad S. Alwan (), Xinzhi Liu () and Taghreed G. Sugati ()
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Mohamad S. Alwan: University of Waterloo, Department of Applied Mathematics
Xinzhi Liu: University of Waterloo, Department of Applied Mathematics
Taghreed G. Sugati: University of Waterloo, Department of Applied Mathematics

A chapter in Mathematical and Computational Approaches in Advancing Modern Science and Engineering, 2016, pp 379-388 from Springer

Abstract: Abstract This paper addresses the problem of exponential stability for a class of switched Switched control singularly perturbed Singularly perturbed systems (SCSPS) not only when all the control actuators are operational, but also when some of them experience failures. Multiple Lyapunov functions Multiple Lyapunov functions and average dwell-time switching signal approach are used to establish the stability criteria for the proposed systems. In this paper, we assume that a full access to all the system modes is available, though the mode-dependent, slow-state feedback controllers experience faulty actuators of an outage type. In the stability analysis, the system under study is viewed as an interconnected system that has been decomposed into isolated, lower order, slow and fast subsystems, and the interconnection between them. It has been observed that if the degree of stability of each isolated mode is greater than the interconnection between them, the interconnected mode is exponentially stable, and, then, the full order SCSPS is also exponentially stable for all admissible switching signals with average dwell-time. A numerical example with simulations is introduced to illustrate the validity of the proposed theoretical results.

Keywords: Reliable Controllers; Multiple Lyapunov Functions; Faulty Actuator; Fast Subsystem; Exponential Stability (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_35

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DOI: 10.1007/978-3-319-30379-6_35

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