Dynamics of hybrid systems induced by operator valued measures

In this paper we consider a class of hybrid systems induced by operator valued measures. This includes semigroups of operators perturbed by bounded as well as unbounded operator valued measures. We construct an evolution operator for the hybrid system and based on its properties we prove existence, uniqueness and regularity properties of solutions. We also consider Semilinear Problems driven by vector measures. Nonstandard problems arising in the study of the classical linear quadratic regulator problem in the present setting are discussed and partial solutions provided.