Title :
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
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;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2005.854582
