Perturbation bounds for coupled matrix Riccati equations

Perturbation Analysis of Coupled Matrix Riccati Equations

Local and non local perturbation bounds for real continuous time coupled algebraic matrix Riccati equations are deriv ed using the technique of Ly apunov majorants and xed point principles Equations of this type arise in the robust analysis and design of linear control systems

Coupled matrix Riccati equations in minimal cost variance control problems

We present an algorithm for the solution of a nontrivial coupled system of algebraic Riccati equations appearing in risk sensitive control problems. Moreover we use comparison methods to derive non blow up conditions for the solutions of a corresponding terminal value problem for coupled systems of Riccati di erential equations.

GIP integrators for Matrix Riccati Differential Equations

Matrix Riccati Differential Equations (MRDEs) are initial value problems of the form: X 0 1⁄4 A21 XA11 þ A22X XA12X; Xð0Þ 1⁄4 X0: These equations arise frequently throughout applied mathematics, science, and engineering. It can happen that even when the Aij are smooth functions of t or constant, the solution X may have a singularity or even infinitely many singularities. This paper shows severa...

Trace Inequalities for Matrix Products and Trace Bounds for the Solution of the Algebraic Riccati Equations

By using diagonalizable matrix decomposition and majorization inequalities, we propose new trace bounds for the product of two real square matrices in which one is diagonalizable. These bounds improve and extend the previous results. Furthermore, we give some trace bounds for the solution of the algebraic Riccati equations, which improve some of the previous results under certain conditions. Fi...

Perturbation theory for Hamiltonian operator matrices and Riccati equations