Input-to-state stability for discrete-time nonlinear systems

Zhong Ping Jiang, Yuan Wang

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)857-869
Number of pages13
Issue number6
StatePublished - Jun 2001


  • Discrete time systems
  • Input-to-state stability
  • Lyapunov functions
  • Nonlinear small-gain
  • Nonlinear stability

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering


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