Existence and uniqueness of solutions for a class of piecewise linear dynamical systems Original Research Article

We consider the class of dynamical systems that arises when inputs and outputs of a linear system are connected pairwise by means of piecewise linear algebraic relations. It is not assumed that these relations define inputs in terms of outputs or vice versa; in particular, the relations need not be Lipschitzian. We obtain conditions for existence and uniqueness of solutions of such dynamical systems in the class of piecewise Bohl functions.