Setting of the problem and state equation

Then, in §4, we show (introducing a class of approximated problems) that the above definition of solution of Riccati equation allows us to characterize, by the dynamic pro­ gramming approach, the optimal state and control, both in the finite and infinite horizon case. In particular we prove that the dynamic system is mean-square stabilizable if and only if there exists a self-adjoint, non negative linear operator X such that X = T(X ) (that is a positive solution of the so called “Algebraic Riccati Equation”).