Stabilizing solutions of the H∞ algebraic Riccati equation

CaSaR 93 - 25 Stabilizing solutions of the H oo algebraic Riccati equation

The algebraic Riccati equation studied in this paper is related to the suboptimal state feedback Hoo control problem. It is parameterized by the Hoo norm bound 'Y we want to achieve. The objective of this paper is to study the behaviour of the solution to the Riccati equation as a function of 'Y. It turns out that a stabilizing solution exists for all but finitely many values of'Y larger than s...

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...

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.

Existence Condition on Solutions to the Algebraic Riccati Equation

First, the existence conditions on the solutions to the algebraic Riccati equation are reviewed. Then, a strict proof is presented for a necessary and sufficient condition on the existence of a unique optimal positive definite solution to this equation. By using this condition, some untrue results on the design of robust decentralized controllers are corrected.