Linear Complementarity Systems with Singleton Properties: Non-Zenoness
Jinglai Shen
Jong-Shi Pang
Univ. of Maryland, Baltimore;
This paper appears in: American Control Conference, 2007. ACC '07
Publication Date: 9-13 July 2007
On page(s): 2769-2774
Location: New York, NY,
ISSN: 0743-1619
ISBN: 1-4244-0988-8
INSPEC Accession Number: 9886343
Digital Object Identifier: 10.1109/ACC.2007.4282333
Current Version Published: 2007-07-30
Abstract
Extending our previous work on linear complementarity systems (LCSs) with the P-property, this paper establishes that a certain class of LCSs of the positive semidefinite-plus type does not have Zeno states. An intrinsic feature of such an LCS is that it has a unique continuously differentiable state solution for any initial condition, albeit the associated algebraic linear complementarity problem has non- unique solutions. Applications of our results to constrained dynamic optimization, and more generally, to differential afHne complementarity systems are discussed. The cornerstone of our proof of the main non-Zeno result is a recent theory for conewise linear systems.
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