Condition numbers of algebraic Riccati equations in the Frobenius norm

Perturbation analysis and condition numbers of symmetric algebraic Riccati equations

This paper is devoted to the perturbation analysis of symmetric algebraic Riccati equations. Based on our perturbation analysis, the upper bounds for the normwise,mixed and componentwise condition numbers are presented. The results are demonstrated by our preliminary numerical experiments. © 2008 Elsevier Ltd. All rights reserved.

Structured Condition Numbers of Symmetric Algebraic Riccati Equations

This paper presents a structured perturbation analysis of the symmetric algebraic Riccati equations by exploiting the symmetry structure. Based on the analysis, structured normwise, componentwise, and mixed condition numbers are defined and their explicit expressions are derived. Due to the exploitation of the symmetry structure, our results are improvements of previous work on the perturbation...

Structured condition numbers and small sample condition estimation of symmetric algebraic Riccati equations

This paper is devoted to a structured perturbation analysis of the symmetric algebraic Riccati equations by exploiting the symmetry structure. Based on the analysis, the upper bounds for the structured normwise, mixed and componentwise condition numbers are derived. Due to the exploitation of the symmetry structure, our results are improvements of the previous work on the perturbation analysis ...

Algebraic Riccati equations

Algebraic Properties of Riccati equations

In this paper we examine the question when the LQR Riccati equation for matrices with components in a subalgebra A of L(H), where H is a Hilbert space, will have a unique nonnegative exponentially stabilizing solution with components in A. We give counterexamples to results claimed in the literature and some positive results for 2× 2 matrices. In addition, we pose a conjecture and an algebraic ...