Perturbation bounds for coupled matrix Riccati equations (Q1864973)

The paper presents a complete local and non-local perturbation analysis of the real continuous-time coupled algebraic matrix Riccati equations (CCAREs) of the form \(F_{i}(X_{1},X_{2},P_{i})=0,i=1,2\) where \(F_{i}\) are matrix quadratic functions in the unknown matrices \(X_{i}\), and \(P_{i}\) are collection of matrix coefficients. CCAREs of this type arise naturally in \( H_{2}/H_{\infty }\) analysis and design of linear control systems. The techniques that have been used are the Lyapunov majorants and fixed point principles. Finally, an experimental analysis is made to compare the performance of the proposed perturbation bounds. The techniques for the perturbation analysis, as well as the perturbation bounds that have been derived, may be extended to other more general systems of matrix quadratic equations.