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Existence and uniqueness of unmixed solutions of the discrete-time algebraic Riccati equation |
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| Authors: | David J. Clements Harald K. Wimmer |
| Affiliation: | a School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney 2052, NSW, Australia b Mathematisches Institut, Universität Würzburg, Am Hubland, D-97074, Würzburg, Germany |
| Abstract: | A solution X of a discrete-time algebraic Riccati equation is called unmixed if the corresponding closed-loop matrix Φ(X) has the property that the common roots of det(sI−Φ(X)) and det(I−sΦ(X)*) (if any) are on the unit circle. A necessary and sufficient condition is given for existence and uniqueness of an unmixed solution such that the eigenvalues of Φ(X) lie in a prescribed subset of . |
| Keywords: | Discrete-time algebraic Riccati equation Unmixed solutions Popov function Closed-loop matrix |
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