Dissipative systems and complementarity conditions

Author

Heemels, W.P.M.H. ; Schumacher, J.M. ; Weiland, S.

Author_Institution

Dept. of Electr. Eng., Eindhoven Univ. of Technol., Netherlands

Volume

4

fYear

1998

fDate

16-18 Dec 1998

Firstpage

4127

Abstract

In this paper existence and uniqueness of solutions to linear complementarity systems (LCS) are considered. Complementarity systems are systems that are composed of differential equations, inequalities and switching logic. These systems can therefore be seen as a subclass of hybrid dynamical systems. The main result of this paper states that dissipativity of the underlying state space description of a LCS is a sufficient condition for existence of so-called initial solutions and guarantees uniqueness of the state trajectory. Applications of the results include electrical networks with diodes

Keywords

differential equations; linear network analysis; linear programming; linear systems; switching functions; system theory; LCS; LTI systems; differential equations; diodes; dissipative systems; electrical networks; hybrid dynamical systems; inequalities; initial solutions; linear complementarity systems; linear time-invariant dynamical systems; state space description; state trajectory uniqueness; switching logic; Differential equations; Diodes; Friction; Logic; Mathematical programming; Mechanical systems; Piecewise linear techniques; Relays; State-space methods; Sufficient conditions;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1998. Proceedings of the 37th IEEE Conference on

Conference_Location

Tampa, FL

ISSN

0191-2216

Print_ISBN

0-7803-4394-8

Type

conf

DOI

10.1109/CDC.1998.761949

Filename

761949