Riccati equations

Algebraic Riccati equations

Riccati Equations in Delay Systems

We give an overview of how the Riccati equation makes its appearance in the stability analysis of linear systems with delays. We avoid complexities as time-invariance, added perturbations, distributed delays etc, to get to the main issues. Most generalizations can be or have been carried out, but do not add substantially to our understanding. We also show the connection between quadratic stabil...

Reproducing Kernels and Riccati Equations

The purpose of this article is to present a brief exposition of the role of Riccati equations in the theory of reproducing kernel spaces. In particular, we shall exhibit a connection between positive semidefinite solutions of matrix Riccati equations and a class of finite dimensional reproducing kernel Hilbert spaces of rational vector valued functions, and an analogous (but more general) conne...

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 ...

On solving periodic Riccati equations

Numerically reliable algorithms to compute the periodic non-negative definite stabilizing solutions of the periodic differential Riccati equation (PRDE) and discrete-time periodic Riccati equation (DPRE) are proposed. For the numerical solution of PRDEs, a new multiple shooting-type algorithm is developed to compute the periodic solutions in an arbitrary number of time moments within one period...