A new class of nonsymmetric algebraic Riccati equations

Motivated by the study of linear quadratic differential games, we introduce a new class of nonsymmetric algebraic Riccati equations. It is shown that every equation in this class has a unique stabilizing solution, which is the solution required to find the open-loop Nash equilibrium for the differential game. We show that the doubling algorithm can be used to find this solution efficiently. The solution may also be found by the Schur method, and under further assumptions by Newton’s method and a basic fixed-point iteration.