Stabilization of discrete-time nonlinear systems by smooth state feedback

Christopher I. Byrnes, Wei Lin, Bijoy K. Ghosh

Research output: Contribution to journalArticlepeer-review

41 Scopus citations


For a class of nonlinear discrete-time systems of the form Σ: x(k+1)=f{hook}(x(k))+g(x(k))u(k), we investigate conditions under which a nonlinear system can be rendered globally asymptotically stable via smooth state feedback. Our main result is that any nonlinear system with Lyapunov-stable unforced dynamics can always be globally stabilized by smooth state feedback if suitable controllability-like rank conditions are satisfied. Several examples are presented to demonstrate the applications of the stability results developed in this paper.

Original languageEnglish
Pages (from-to)255-263
Number of pages9
JournalSystems and Control Letters
Issue number3
StatePublished - Sep 1993


  • Discrete-time nonlinear systems
  • critical problems of stabilization
  • linear approximation
  • local and global asymptotic stabilization
  • smooth state feedback


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