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

Bin Liu, Bo Xu, Guohua Zhang and Lisheng Tong
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Bin Liu: College of Science, Hunan University of Technology, Zhuzhou 412000, China
Bo Xu: College of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou 412000, China
Guohua Zhang: College of Science, Hunan University of Technology, Zhuzhou 412000, China
Lisheng Tong: College of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou 412000, China

Mathematics, 2019, vol. 7, issue 12, 1-28

Abstract: 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.

Keywords: impulsive systems; stochastic impulsive systems; impulsive hybrid systems; uniform stability; input-to-state stability; event-stability; Lyapunov function; average dwell-time; time-delay (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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