An Invariance Principle for Nonlinear Discrete Autonomous Dynamical Systems

This note proposes an extension of LaSalle's invariance principle for nonlinear discrete autonomous dynamical systems. The invariance principle is extended to allow the first difference of the auxiliar scalar function (usually a Lyapunov function) to be positive in some bounded regions. Moreove...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2007-04, Vol.52 (4), p.692-697
Main Authors: Alberto, L.F.C., Calliero, T.R., Martins, A.C.P.
Format: Article
Language:English
Subjects:
Applied sciences
Asymptotic stability
Autonomous
Computer science
control theory
systems
Control theory. Systems
Difference equations
Differential equations
Discrete systems
Dynamical systems
Estimates
Exact sciences and technology
Invariance
invariance principle
Lyapunov functions
Lyapunov method
Nonlinearity
Power system stability
Scalars
Stability
Stability analysis
Switched systems
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Summary:This note proposes an extension of LaSalle's invariance principle for nonlinear discrete autonomous dynamical systems. The invariance principle is extended to allow the first difference of the auxiliar scalar function (usually a Lyapunov function) to be positive in some bounded regions. Moreover, a uniform version is proposed to deal with nonlinear discrete dynamical systems that vary with parameters. Both extensions have the original invariance principle as a particular case. As a consequence, a larger class of systems can be treated with this new theory. The extensions are very useful to obtain attractor estimates as well as their corresponding stability regions. The uniform version, in particular, is useful to obtain estimates that are uniform regarding parameters
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2007.894532