A Parametrization of Solutions of the Discrete-time Algebraic Riccati Equation Based on Pairs of Opposite Unmixed Solutions

Authors:
Harald K. Wimmer
Affiliations:
-
Venue:
SIAM Journal on Control and Optimization
Year:
2006

Citing 0
Cited 2

General Matrix Pencil Techniques for Solving Discrete-Time Nonsymmetric Algebraic Riccati Equations

SIAM Journal on Matrix Analysis and Applications
Characterization of Exponential Divergence of the Kalman Filter for Time-Varying Systems

SIAM Journal on Control and Optimization

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Abstract

The paper describes the set of solutions of the discrete-time algebraic Riccati equation. It is shown that each solution is a combination of a pair of opposite unmixed solutions. There is a one-to-one correspondence between solutions and invariant subspaces of the closed loop matrix of an unmixed solution. The results of the paper provide an extended counterpart of the parametrization theory of continuous-time algebraic Riccati equations by Willems, Coppel, and Shayman.