Journal
AUTOMATICA
Volume 37, Issue 6, Pages 857-869Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/S0005-1098(01)00028-0
Keywords
nonlinear stability; discrete lime systems; Lyapunov functions; input-to-state stability; nonlinear small-gain
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In this work we study the input-to-state stability (ISS) property for discrete-time nonlinear systems. It is shown that most Iss results for continuous-time nonlinear systems in the current literature can be extended to the discrete-time case. Several equivalent characterizations of ISS are introduced and two ISS small-gain theorems are proved for nonlinear and interconnected discrete-time systems. ISS stabilizability is discussed and comparisons with the continuous-time case are made. As in the continuous time framework, where the notion Iss found wide applications, we expect that this notion will provide a useful tool in areas related to stability and stabilization for nonlinear discrete time systems as well. (C) 2001 Elsevier Science Ltd. All rights reserved.
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