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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].

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