Small-gain theorem for ISS systems and applications

Zhong-Ping Jiang, A. R. Teel, L. Praly

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)95-120
Number of pages26
JournalMathematics of Control, Signals, and Systems
Volume7
Issue number2
DOIs
StatePublished - Jun 1994

Fingerprint

Small Gain Theorem
Practical Stability
System stability
Output
Identity function
State feedback
State Feedback
Interconnection
Linear systems
Stabilization
Assignment
Linear Systems
Perturbation
Feedback
Partial
Chemical analysis

Keywords

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

ASJC Scopus subject areas

  • Applied Mathematics
  • Electrical and Electronic Engineering
  • Signal Processing

Cite this

Small-gain theorem for ISS systems and applications. / Jiang, Zhong-Ping; Teel, A. R.; Praly, L.

In: Mathematics of Control, Signals, and Systems, Vol. 7, No. 2, 06.1994, p. 95-120.

Research output: Contribution to journalArticle

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