Isolated semidefinite solutions of the continuous-time 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...

Intervals of solutions of the discrete-time algebraic Riccati equation

If two solutions Y ≤ Z of the DARE are given then the set of solutions X with Y ≤ X ≤ Z can be parametrized by invariant subspaces of the closed loop matrix corresponding to Y . The paper extends the geometric theory of Willems from the continuous-time to the discrete-time ARE making the weakest possible assumptions.

The Descriptor Continuous-Time Algebraic Riccati Equation. Numerical Solutions and Some Direct Applications

We investigate here the numerical solution of a special type of descriptor continuous-time Riccati equation which is involved in solving several key problems in robust control, formulated under very general hypotheses. We also give necessary and sufficient existence conditions together with computable formulas for both stabilizing and antistabilizing solutions in terms of the associated matrix ...

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...

A Geometric Characterization of Solutions to The Algebraic Riccati Equation