Stabilization and robustness analysis for a chain of exponential integrators using strict Lyapunov functions

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• 作者：Michael Malisoff^a ; ^{malisoff@lsu.edu" class="auth_mail" title="E-mail the corresponding author}Author Vitae ; Miroslav Krstic^b ; ¹ ; ^{krstic@ucsd.edu" class="auth_mail" title="E-mail the corresponding author}Author Vitae
• 关键词：Strict Lyapunov functions ; Input-to-state stability
• 刊名：Automatica
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：68
• 期：Complete
• 页码：184-193
• 全文大小：591 K

文摘

We provide a new method for building strict Lyapunov functions for two dimensional chains of exponential integrators, using nested exponential functions. One challenge is that the right sides of the systems saturate, so they are not completely controllable. The strictness of the Lyapunov functions is key to proving input-to-state stability (or ISS) properties with respect to additive uncertainty on the controls. We show how a large class of tracking problems for nonlinear systems with positivity constraints on the states can be solved using our theory.