On the Existence of a Stabilizing Solution of Modified Algebraic Riccati Equations in Terms of Standard Algebraic Riccati Equations and Linear Matrix Inequalities

In this letter, we study conditions for the existence of stabilizing solutions of two classes of modified discrete algebraic Riccati equations (MAREs) emerging in stochastic control problems. In order to do so, we first rewrite each MARE in terms of a standard ARE subject to specific constraints, which allows us to connect their solution with a set of linear-control constrained problems. With this result we also determine, for each MARE, a linear matrix inequality problem whose feasibility is guaranteed if and only if a stabilizing solution of the original MARE exists.