Discrete Riccati equation solutions: Distributed algorithms

Solutions of the Riccati equation for H Discrete Time Systems

Let H and Y be separable Hilbert spaces, and U finite dimensional. Let A ∈ L(H), B ∈ L(U,H), C ∈ L(H,Y ), D ∈ L(U, Y ), and suppose that the open loop transfer function D(z) := D+zC(I−zA)B ∈ H(D;L(U, Y )), where D is the open unit disk. We consider a subset of self adjoint solutions P of the discrete time algebraic operator Riccati equation (DARE)    APA− P + CJC = K PΛPKP , ΛP = D JD +BPB...

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.

Perturbation analysis of the discrete Riccati equation

The sensitivity of the discrete-time matrix Riccati equation relative to perturbations in its coefficients is studied. Both local and non-local perturbation bounds are obtained. In particular the conditioning of the equation is determined.

The discrete Riccati equation of optimal control

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...