### Finite-Time Lyapunov Functions and Impulsive Control Design

Huijuan Li, Qingxia Ma, Yongjian Liu
<span title="2020-10-27">2020</span> <i title="Hindawi Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/y3fh56bfunh5fgneywwba6d4ke" style="color: black;">Complexity</a> </i> &nbsp;
In this paper, we introduce finite-time Lyapunov functions for impulsive systems. The relaxed sufficient conditions for asymptotic stability of an equilibrium of an impulsive system are given via finite-time Lyapunov functions. A converse finite-time Lyapunov theorem for controlling the impulsive system is proposed. Three examples are presented to show how to analyze the stability of an equilibrium of the considered impulsive system via finite-time Lyapunov functions. Furthermore, according to
more &raquo; ... he results, we design an impulsive controller for a chaotic system modified from the Lorenz system.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2020/5179752">doi:10.1155/2020/5179752</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6pir6pp4qjfs5owjtv6g26koh4">fatcat:6pir6pp4qjfs5owjtv6g26koh4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20201029212547/http://downloads.hindawi.com/journals/complexity/2020/5179752.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/25/f9/25f9fa76562afc99e4abb31be11d8aeab7679214.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2020/5179752"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> hindawi.com </button> </a>