Pick Matrix Conditions for Sign-Definite Solutions of the Algebraic Riccati Equation

Solving the Algebraic Riccati Equation with the Matrix Sign Function

This paper presents solne inrprovements to the matrix-sigll-fllnction algorithn~ for the alge\,raic Riccati equation. A simple reorganization changes nonsynnnetric watrix inversion5 into syinmetric niatrix inversions. Scaling accelerates convergence of the basic iteration ant1 yields a new qnadratic formula for certain 2-by-2 algebraic Riccati eqnation5. Numerical experience suggests the algori...

All unmixed solutions of the algebraic Riccati equation using Pick matrices

In this short paper we study the existence of positive and negative semide nite solutions of the algebraic Riccati equation corresponding to linear quadratic problems with an inde nite cost functional. An important role is played by certain two-variable polynomial matrices associated with the algebraic Riccati equation. We characterize al unmixed solutions in terms of the Pick matrices associat...

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...

A Geometric Characterization of Solutions to The Algebraic Riccati Equation

Isolated Semidefinite Solutions of the Continuous-time Algebraic Riccati Equation

where A,B and C are complex matrices of dimensions n × n, n × p and q × n respectively. We focus on the set T = {X | R(X) = 0, X ≤ 0} of negative-semidefinite solutions and we shall characterize those elementsX of T which are isolated (in the topology which T inherits as a subset of the normed space C n×n). Such an isolated X has the property that for a sufficiently small there is no solution Y...