Robust verification algorithm for stabilizing solutions of discrete-time algebraic Riccati equations

Abstract

A robust algorithm is proposed for numerically computing an interval matrix containing the stabilizing solution of a discrete-time algebraic Riccati equation. This algorithm is based on estimating an upper bound for the spectral radius of a matrix power utilizing the Perron–Frobenius theory. The algorithm moreover verifies the uniqueness of the contained solution. Numerical results show that the algorithm is more successful than the previous algorithms.