Abstract
We study discrete algebraic matrix Riccati equations arising in robust control and filtering problems based on its associated symplectic matrix and Popov function. Necessary and sufficient conditions are established for the existence of a stabilizing solution, which in contrast to standard equations arising in LQG problems is not necessarily nonnegative-definite. Then the existence conditions are shown for nonnegative-definite, and positive-definite stabilizing solutions both as necessary and sufficient conditions. Next, parallel results are established for the existence of the so-called anti-stabilizing solution, and a relation between stabilizing and anti-stabilizing solutions of original and dual Riccati equations is shown. It is also proved that stabilizing and anti-stabilizing solutions if they exist are the minimal and maximal solutions respectively.
