Abstract
In this paper, algebraic matrix Riccati equations are analyzed that have nonnegative-definite quadratic as well as constant terms, employing the so-called algebraic method. Necessary and sufficient conditions are established for the existence of stabilizing solution, which is not necessarily nonnegative-definite unlike the case of standard equations arising in LQG problems. Nonnegative-definite stabilizing solution is shown to exist if and only if the system is asymptotically stable and the H ∞ norm of transfer matrix be less than one. For positive-definite solution, we need additional condition that the system be controllable. Next necessary and sufficient conditions are established for the existence of the so-called anti-stabilizing solution for both general and positive-definite cases. It is shown that stabilizing solution is minimal existence of nonnegative-definite stabilizing solution, all the other (hence nonnegative-definite) solutions with lattice structure are derived, together with the number of nonnegative-definite solutions.
