Nonnegative solutions of algebraic Riccati equations

Structure-preserving algorithms for Hermitian solutions of algebraic Riccati equations

In this paper, we propose structure-preserving algorithms for the computation of Hermitian solutions of continuous/discrete-time algebraic Riccati equations. Under assumptions that partial multiplicities of purely imaging and unimodular eigenvalues (if any) of the associated Hamiltonian and symplectic pencil, respectively, are all even, we prove that the developed structure-preserving algorithm...

Accurate solutions of M-matrix algebraic Riccati equations

This paper is concerned with the relative perturbation theory and its entrywise relatively accurate numerical solutions of an M -matrix Algebraic Riccati Equations (MARE) XDX −AX −XB + C = 0 by which we mean the following conformally partitioned matrix ( B −D −C A ) is a nonsingular or an irreducible singular M -matrix. It is known that such an MARE has a unique minimal nonnegative solution Φ. ...

Algebraic Riccati equations

Methods for Verified Solutions to Continuous-time Algebraic Riccati Equations

We describe a procedure based on the Krawczyk method to compute a verified enclosure for the stabilizing solution of a continuoustime algebraic Riccati equation A∗X + XA + Q = XGX, building on the work of [B. Hashemi, SCAN 2012] and adding several modifications to the Krawczyk procedure. Moreover, we describe a new O(n) direct method for verification, based on a fixed-point formulation of the e...

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 ...