Small-gain theorem for ISS systems and applications

  • Z. -P. Jiang
  • A. R. Teel
  • L. Praly


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.

Key words

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


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Copyright information

© Springer-Verlag London Limited 1994

Authors and Affiliations

  • Z. -P. Jiang
    • 1
  • A. R. Teel
    • 2
  • L. Praly
    • 1
  1. 1.Centre Automatique et SystèmesEcole des Mines de ParisFontainebleau cédexFrance
  2. 2.Department of Electrical EngineeringUniversity of MinnesotaMinneapolisUSA

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