A representation of all bounded self-adjoint solutions of the algebraic Riccati equation for systems with an unbounded observation operator

In this paper a representation of all bounded self-adjoint solutions of the control algebraic Riccati equation associated to the infinite-dimensional well-posed linear system Σ(A,B,C) with an unbounded observation operator is obtained. The assumptions imposed on the systems are: A generates a C₀-group, the system is output stabilizable, strongly detectable and the dual Riccati equation has an invertible bounded nonnegative solution.