Extended algebraic Riccati equations in the abstract hyperbolic case
The optimal quadratic cost problem over an infinite (time) horizon, and related algebraic Riccati equation, associated with an abstract equation is extended subject to the hypothesis of the abstract hyperbolic dynamics, in particular, with a fully unbounded control operator. This problem is studied, in full generality, in the abstract hyperbolic setting, following the treatment by abstract methods of the concrete, canonical case of a second-order hyperbolic equation.
Nonlinear Analysis, Theory, Methods and Applications
Barbu, V., Lasiecka, I., & Triggiani, R. (2000). Extended algebraic Riccati equations in the abstract hyperbolic case. Nonlinear Analysis, Theory, Methods and Applications, 40 (1), 105-129. https://doi.org/10.1016/S0362-546X(00)85007-5