Nonautonomous Linear-Quadratic Dissipative Control Processes Without Uniform Null Controllability

作者：Johnson Russell; Novo Sylvia^*; Nunez Carmen; Obaya Rafael

来源：Journal of Dynamics and Differential Equations, 2017, 29(2): 355-383.

DOI：10.1007/s10884-015-9495-1

• Nonautonomous linear Hamiltonian systems
• Linear-quadratic control system
• Dissipativity
• Abnormal system
• Rotation number
• Proper focal point

In this paper the dissipativity of a family of linear-quadratic control processes is studied. The application of the Pontryagin Maximum Principle to this problem gives 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. Sufficient 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 systems or by a convenient disconjugate perturbation of it.

• 出版日期2017-6