Hamiltonians and Riccati equations for linear systems with unbounded control and observation operators (Q2910914)

This paper is concerned with the algebraic Riccati equation NEWLINE\[NEWLINEA^{*}X+XA-XBB^{*}X+C^{*}C=0.NEWLINE\]NEWLINE The minimal nonnegative solution of this problem determines the optimal cost, and \(-B^{*}X\) is the optimal feedback. The authors construct the selfadjoint solutions of the control algebraic Riccati equation by using invariant subspaces of the associated Hamitonian. The results are applicable to infinite-dimensional systems whose generators are normal and have a compact resolvent and whose control and observation operators are possibly unbounded.