Stability analysis of discontinuous dynamical systems determined by semigroups

Author

Michel, Anthony N. ; Sun, Ye ; Molchanov, Alexander P.

Author_Institution

Dept. of Electr. Eng., Univ. of Notre Dame, IN, USA

Volume

50

Issue

9

fYear

2005

Firstpage

1277

Lastpage

1290

Abstract

We present Lyapunov stability results for discontinuous dynamical systems (DDS) determined by linear and nonlinear semigroups defined on Banach space. DDS of the type considered herein arise in the modeling of a variety of finite- and infinite-dimensional systems, including certain classes of hybrid systems, discrete-event systems, switched systems, systems subjected to impulse effects, and the like. We apply our results in the analysis of several important specific classes of DDS.

Keywords

Banach spaces; Lyapunov methods; discrete event systems; group theory; multidimensional systems; sampled data systems; stability; time-varying systems; Banach space; Lyapunov stability; asymptotic stability; discontinuous dynamical system; discrete-event system; exponential stability; finite-dimensional system; functional differential equations; heat equation; hybrid system; infinite-dimensional system; linear semigroups; nonlinear semigroups; partial differential equation; stability analysis; switched system; Differential equations; Discrete event systems; Extraterrestrial measurements; Lyapunov method; Nonlinear equations; Partial differential equations; Stability analysis; Sun; Switched systems; Vectors; Asymptotic stability; Lyapunov stability; discontinuous dynamical systems (DDS); exponential stability; functional differential equations; heat equation; nonlinear semigroups; partial differential equations;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2005.854582

Filename

1506936