Existence and Numerical Solution for Norm-Type Algebraic Riccati Equations

Abstract

This paper considers a continuous algebraic Riccati equation with an additional norm-type term. This equation is called a norm-type algebraic Riccati equation and arises in guaranteed cost control on the basis of a norm-type upper bound. It is shown that there exists a solution under the stabilizability condition and the assumption that the additional term is not too large. Also, the well-known Kleinman's algorithm is extended to this case.