Stability of Hybrid Singularly Perturbed Systems with Time Delay

[摘要] Hybrid singularly perturbed systems (SPSs) with time delay are considered and exponential stability of these systems is investigated. This work mainly covers switched and impulsiveswitched delay SPSs . Multiple Lyapunov functions technique as a tool is applied to these systems. Dwell and average dwell timeapproaches 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 ofall unstable subsystems are also established. A number of illustrative examples are presented to help motivate the study of these systems.

[发布机构] University of Waterloo

[效力级别] Stability

[关键词] Mathematics;Stability;Hybrid systems;Singular perturbation;Time delay