Solving Parametrized Non-symmetric Algebraic Riccati Equations: A Matrix Sign Function Approach

Abstract

We study numerical solutions of parameterized non--symmetric continuous--time algebraic Riccati equations (PNAREs) related to issues in control system theory and differential games. Thanks to good regularity properties of the solutions of PNAREs with respect to the parameter, our main tool involving an analytically determined matrix sign function is applied to the computation of various solutions, including the strongly stabilizing, the reverse dichotomic and the dichotomic ones.  The efficiency of the proposed method is illustrated by several numerical experiments.