| A converse Lyapunov theorem and input-to-state stability properties for discrete-time nonlinear systems (2007) | |||||||||||||||||
Abstract | |||||||||||||||||
| In this work we study the input-to-state stability (ISS) property for discrete-time nonlinear systems. We first establish a converse Lyapunov theorem for robust global asymptotic stability in discrete-time. Then, 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. | |||||||||||||||||
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