Linear Complementarity Systems with Singleton Properties: Non-Zenoness

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.