Properties of solutions of quaternionic Riccati equations

Improving the Accuracy of the Solutions of Riccati Equations

Continuity properties of solutions to H2 and H∞ Riccati equations

In most H2 and H∞ control problems solutions of the algebraic Riccati equation play a crucial role. Note that in general for continuous time systems we have to use quadratic matrix inequalities instead of Riccati equations. For details we refer to [5]. In particular we are interested in the stabilizing solution of these Riccati equations and quadratic matrix inequalities. However, if the system...

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 ...

Approximation of Solutions of Riccati Equations

This paper deals with two interrelated issues. One is an invariant subspace approach to finding solutions for the algebraic Riccati equation for a class of infinite dimensional systems. The second is approximation of the solution of the algebraic Riccati equation by finite dimensional approximants. The theory of exponentially dichotomous operators and bisemigroups is instrumental in our approach.

Analytic properties of matrix Riccati equation solutions

For matrix Riccati equations of platoontype systems and of systems arising from PDEs, assuming the coefficients are analytic functions in a suitable domain, the analyticity of the stabilizing solution is proved under various hypotheses. In addition, general results on the analytic behavior of stabilizing solutions are developed. I. NONSTANDARD RICCATI EQUATIONS In [10], [7] and elsewhere contin...