Reorienting linear complementarity systems using feedback

Abstract

Unlike linear dynamical systems the existence and uniqueness of solutions (wellposedness) for linear complementarity systems (LCS) is not trivial. It has been shown in literature that the consistent and jump space of an LCS (with zero input) plays an important role in establishing the wellposedness. In this paper we apply state and port feedback to an LCS to reorient these spaces. Sometimes it is desirable to increase the consistent space which means enlarging the set of states having continuous extension. At the same time it may be desirable to shrink the set of states which may have discontinuous extension, in other words, to decrease the jump space. Sufficient conditions in this direction are obtained in terms of feedback matrices.