%0 Book Section
%A Bemporad, Alberto
%A Borrelli, Francesco
%A Morari, Manfred
%B Hybrid Systems: Computation and Control
%D 2002
%F eprints:524
%I Springer-Verlag
%P 105-119
%T On the optimal control law for linear discrete time hybrid systems
%U http://eprints.imtlucca.it/524/
%V 2289
%X In this paper we study the solution to optimal control problems for discrete time linear hybrid systems. First, we prove that the closed form of the state-feedback solution to finite time optimal control based on quadratic or linear norms performance criteria is a time-varying piecewise afine feedback control law. Then, we give an insight into the structure of the optimal state-feedback solution and of the value function. Finally, we briefly describe how the optimal control law can be computed by means of multiparametric programming.