Small-gain theorem for ISS systems and applications

Z. P. Jiang, A. R. Teel, L. Praly

Research output: Contribution to journalArticlepeer-review


We introduce a concept of input-to-output practical stability (IOpS) which is a natural generalization of input-to-state stability proposed by Sontag. It allows us to establish two important results. The first one states that the general interconnection of two IOpS systems is again an IOpS system if an appropriate composition of the gain functions is smaller than the identity function. The second one shows an example of gain function assignment by feedback. As an illustration of the interest of these results, we address the problem of global asymptotic stabilization via partial-state feedback for linear systems with nonlinear, stable dynamic perturbations and for systems which have a particular disturbed recurrent structure.

Original languageEnglish (US)
Pages (from-to)95-120
Number of pages26
JournalMathematics of Control, Signals, and Systems
Issue number2
StatePublished - Jun 1994


  • Global stability
  • Input-to-state stability
  • Nonlinear systems
  • Partial-state feedback

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Signal Processing
  • Control and Optimization
  • Applied Mathematics


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