Abnormal linear hamiltonian systems with application in non-autonomous linear-quadratic control processes.
In this talk the dissipativity of a family of non-autonomous linear-quadratic control processes is studied using methods of topological dynamics. The application of the Pontryaguin Maximum Principle to this problem give rise to a family of linear Hamiltonian systems for which the existence of an exponential dichotomy is assumed, but no condition of controllability is imposed. As a consequence, some of the systems of this family could be abnormal and some of their dynamical properties are given. Sufficiente conditions for the dissipativity of the processes are provided assuming the existence of global positive solutions of the Riccati equation induced by the family of linear hamiltonian sytems or by a conveniente disconjugate perturbation of it.