THE CONTACT PROBLEM FOR LINEAR CONTINUOUS-TIME DYNAMICAL-SYSTEMS - A GEOMETRIC APPROACH

In this paper linear time-invariant dynamical systems described by a c ombination of differential equalities and static inequalities in state -space formulation are investigated, Of special interest is the contac t problem: the effect of the boundary of the constraint set on the beh avior of the system, This effect is studied by dividing the state-spac e in a number of disjunct subsets, It is shown that these subsets are invariant under linear state feedback, In our framework, a specific pl ace is reserved for modeling the laws of collision, i.e., physical mod eling, which are regarded as external factors, Our main results are a system theoretical framework in which we describe what happens upon co ntact and a definition of the constrained state-space system in terms of its restricted behavior, The results presented here can be consider ed as an extension for restricted linear systems of the classic positi ve invariance theory for linear systems.