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

by Bin Liu 1,*, Bo Xu 2, Guohua Zhang 1,* and Lisheng Tong 2
1
College of Science, Hunan University of Technology, Zhuzhou 412000, China
2
College of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou 412000, China
*
Authors to whom correspondence should be addressed.
Mathematics 2019, 7(12), 1186; https://doi.org/10.3390/math7121186
Received: 7 October 2019 / Revised: 29 October 2019 / Accepted: 5 November 2019 / Published: 4 December 2019
(This article belongs to the Special Issue Impulsive Control Systems and Complexity)
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. View Full-Text
Keywords: impulsive systems; stochastic impulsive systems; impulsive hybrid systems; uniform stability; input-to-state stability; event-stability; Lyapunov function; average dwell-time; time-delay impulsive systems; stochastic impulsive systems; impulsive hybrid systems; uniform stability; input-to-state stability; event-stability; Lyapunov function; average dwell-time; time-delay
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MDPI and ACS Style

Liu, B.; Xu, B.; Zhang, G.; Tong, L. Review of Some Control Theory Results on Uniform Stability of Impulsive Systems. Mathematics 2019, 7, 1186.

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