New results on the stability of discrete-time systems and applications to control problems
type: Item
instance of: scholarly article
title: New results on the stability of discrete-time systems and applications to control problems
zbMATH Open document ID: 0915.93054
author: M. Bensoubaya
author: Abderrahman Iggidr
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-07-12T00:00:00Z
review text: The authors consider nonlinear autonomous discrete-time systems of the form \[ X(k+1)= f(x(k)) \quad f(0)=0. \] The main goal is an extension of LaSalle's invariance principle. The main feature of the result is that, unlike the classical approach, the Lyapunov function is not necessarily required to be positive definite: positive semidefinite suffices. On the set where the Lyapunov function vanishes, an additional condition, which is reminiscent of the center manifold theorem, is needed. The authors present some examples and application to control problems. In particular, they prove stability results for cascade systems and for systems with stable unforced dynamics.
Mathematics Subject Classification ID: 93D20
Mathematics Subject Classification ID: 93C55
Mathematics Subject Classification ID: 93A99
zbMATH DE Number: 1215743
zbMATH Keywords: stability
zbMATH Keywords: nonlinear discrete-time systems
zbMATH Keywords: LaSalle's invariance principle
zbMATH Keywords: Lyapunov function
zbMATH Keywords: center manifold theorem
zbMATH Keywords: cascade systems
reviewed by: Andrea Bacciotti
MaRDI profile type: Publication
OpenAlex ID: W1992031861
cites work: Applications of centre manifold theory
cites work: Q4871718
cites work: Q5584086
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cites work: Q4180709
cites work: Further facts about input to state stabilization
cites work: Decomposition techniques for large-scale systems with nonadditive interactions: Stability and stabilizability
DOI: 10.1006/JMAA.1997.5827
description: scientific article; zbMATH DE number 1215743