An accelerated technique for solving one type of discrete-time algebraic Riccati equations

摘要

Algebraic Riccati equations are encountered in many applications of controland engineering problems, e.g., LQG problems and $H^\infty$ control theory. Inthis work, we study the properties of one type of discrete-time algebraicRiccati equations. Our contribution is twofold. First, we present sufficientconditions for the existence of a unique positive definite solution. Second, wepropose an accelerated algorithm to obtain the positive definite solution withthe rate of convergence of any desired order. Numerical experiments stronglysupport that our approach performs extremely well even in the almost criticalcase. As a byproduct, we provide show that this method is capable of computingthe unique negative definite solution, once it exists.