Review of Some Control Theory Results on Uniform Stability of Impulsive Systems

This paper aims to review some uniform stability results for impulsive systems. For the review, we classify the models of impulsive systems into time-based impulsive systems and state-based ones, including continuous-time impulsive systems, discrete-time impulsive systems, stochastic impulsive syste...

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Bibliographic Details
Published in:Mathematics (Basel) 2019-12, Vol.7 (12), p.1186
Main Authors: Liu, Bin, Xu, Bo, Zhang, Guohua, Tong, Lisheng
Format: Article
Language:English
Subjects:
Control stability
Control theory
Discrete time systems
Dynamical systems
Euclidean space
Hybrid systems
Mathematics
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Summary:This paper aims to review some uniform stability results for impulsive systems. For the review, we classify the models of impulsive systems into time-based impulsive systems and state-based ones, including continuous-time impulsive systems, discrete-time impulsive systems, stochastic impulsive systems, and impulsive hybrid systems. According to these models, we review, respectively, the related stability concepts and some representative results focused on uniform stability, including the results on uniform asymptotic stability, input-to-state stability (ISS), KLL -stability (uniform stability expressed by KLL -functions), event-stability, and event-ISS. And we formulate some questions for those not fully developed aspects on uniform stability at each subsection.
ISSN:2227-7390
2227-7390
DOI:10.3390/math7121186