Qualitative equivalences of ISS and -gain stability properties for discrete-time nonlinear systems

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• 作者：Duc N. Tran^a ; ^{DucNgocAnh.Tran@uon.edu.au}Author Vitae ; Christopher M. Kellett^a ; ^{Chris.Kellett@newcastle.edu.au}Author Vitae ; Peter M. Dower^b ; ^{p.dower@unimelb.edu.au}Author Vitae
• 关键词：Input-to-state stability ; Discrete-time systems ; Nonlinear systems
• 刊名：Automatica
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：77
• 期：Complete
• 页码：360-369
• 全文大小：750 K
• 卷排序：77

文摘

Input-to-state stability (ISS) and input–output L2L2-gain are two important robust stability concepts in analyzing the interconnections of nonlinear dynamical systems. In this paper, we demonstrate several qualitative equivalences between different ISS related properties and lplp-gain properties for discrete-time systems via nonlinear changes of coordinates. Prior to that, certain summation-to-summation estimates are shown to be equivalent to the standard definitions of ISS and integral ISS (iISS) which lead to sufficient Lyapunov function conditions to verify lplp-gain properties. Combined with known results on the equivalence of 00-input global asymptotic stability and iISS, and a superposition principle, we subsequently outline interesting implicative relationships between various discrete-time robust stability properties.