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On the numerical solution of the discrete-time periodic Riccati equation. (English) Zbl 0805.65063
Helmke, Uwe (ed.) et al., Systems and networks: mathematical theory and applications. Proceedings of the 10th international symposium on the mathematical theory of networks and systems, MTNS ’93, held in Regensburg, Germany, August 2-6, 1993. Volume II: Invited and contributed papers. Berlin: Akademie Verlag. Math. Res. 79, 713-716 (1994).
Summary: We present a method for the computation of the periodic nonnegative definite stabilizing solution of the periodic Riccati equation. This method simultaneously triangularizes by orthogonal equivalences a sequence of matrices associated with a cyclic pencil formulation related to the Euler-Lagrange difference equations. In so doing, it is possible to extract a basis for the stable deflating subspace of the extended pencil, from which the Riccati solution is obtained. This algorithm is an extension of the standard $$QZ$$ algorithm and retains its attractive features, such as quadratic convergence and small relative backward error.
For the entire collection see [Zbl 0797.00031].

##### MSC:
 65K10 Numerical optimization and variational techniques 93C55 Discrete-time control/observation systems