Title :
An Invariance Principle for Nonlinear Discrete Autonomous Dynamical Systems
Author :
Alberto, Luís F C ; Calliero, Taís R. ; Martins, Andre C P
Author_Institution :
Univ. de Sao Paulo, Sao Carlos
fDate :
4/1/2007 12:00:00 AM
Abstract :
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
Keywords :
Lyapunov methods; discrete systems; invariance; nonlinear dynamical systems; stability; Lyapunov function; auxiliar scalar function; invariance principle; nonlinear discrete autonomous dynamical systems; stability; Asymptotic stability; Difference equations; Differential equations; Lyapunov method; Power system stability; Stability analysis; Switched systems; Discrete systems; invariance principle; stability;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2007.894532