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Small-gain theorem for ISS systems and applications

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Abstract

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.

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Authors and Affiliations

  1. Centre Automatique et Systèmes, Ecole des Mines de Paris, 35 rue St Honoré, 77305, Fontainebleau cédex, France

    Z. -P. Jiang & L. Praly

  2. Department of Electrical Engineering, University of Minnesota, 4-174 EE/CS Building, 200 Union St. SE, 55455, Minneapolis, Minnesota, USA

    A. R. Teel

Authors
  1. Z. -P. Jiang
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  2. A. R. Teel
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  3. L. Praly
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Additional information

The final version of this work was finished when Z.-P. Jiang held a visiting position at I.N.R.I.A., Sophia Antipolis.

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Jiang, Z.P., Teel, A.R. & Praly, L. Small-gain theorem for ISS systems and applications. Math. Control Signal Systems 7, 95–120 (1994). https://doi.org/10.1007/BF01211469

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  • DOI: https://doi.org/10.1007/BF01211469

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