Computation of Lyapunov functions for nonautonomous systems on finite time-intervals by linear programming

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• 作者：Sigurdur F. Hafstein^a ; ^{sigurdurh@ru.is" class="auth_mail" title="E-mail the corresponding author} ; Huijuan Li^b ; ¹ ; ^{huijuanhongyan@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Lyapunov function ; Finite-time Lyapunov function ; Periodic-time system ; Linear programming
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：447
• 期：2
• 页码：933-950
• 全文大小：2828 K

文摘

We present an algorithm for numerically computing Lyapunov functions for nonautonomous systems on finite time-intervals. The algorithm relies on a linear optimization problem and delivers a continuous and piecewise affine function on a compact set. The level-sets of such a Lyapunov function give concrete bounds on the time-evolution of the system on the time-interval and for time-periodic systems they deliver an ultimate bound on solutions. Four examples of computed finite-time Lyapunov functions are given.