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Stability of Hybrid Singularly Perturbed Systems with Time Delay

by Alwan, Mohamad

Abstract (Summary)
Hybrid singularly perturbed systems (SPSs) with time delay are considered and exponential stability of these systems is investigated. This work mainly covers switched and impulsive switched delay SPSs . Multiple Lyapunov functions technique as a tool is applied to these systems. Dwell and average dwell time approaches are used to organize the switching between subsystems (modes) so that the hybrid system is stable. Systems with all stable modes are first discussed and, after developing lemmas to ensure existence of growth rates of unstable modes, these systems are then extended to include, in addition, unstable modes. Sufficient conditions showing that impulses contribute to yield stability properties of impulsive switched systems that consist of all unstable subsystems are also established. A number of illustrative examples are presented to help motivate the study of these systems.
Bibliographical Information:

Advisor:

School:University of Waterloo

School Location:Canada - Ontario

Source Type:Master's Thesis

Keywords:mathematics stability hybrid systems singular perturbation time delay

ISBN:

Date of Publication:01/01/2006

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