caa a22 4500 475838955 CHVBK 20180406123856.0 cr unu---uuuuu 170329e20000501xx s 000 0 eng 10.1023/A:1006405104724 doi (NATIONALLICENCE)springer-10.1023/A:1006405104724 On an Alternative Parameterization of the Solutions of the Partial Realization Problem [Elektronische Daten] [Tony Van Gestel, Marc Van Barel, Bart De Moor] The solutions of the partial realization problem have to satisfy a finite number of interpolation conditions at ∞. The minimal degree of an interpolating deterministic system is called the algebraic degree or McMillan degree of the partial covariance sequence and is easy to compute. The solutions of the partial stochastic realization problem have to satisfy the same interpolation conditions and have to fulfill a positive realness constraint. The minimal degree of a stochastic realization is called the positive degree. In the literature, solutions of the partial realization problem are parameterized by the Kimura-Georgiou parameterization. Solutions of the partial stochastic realization problem are then obtained by checking the positive realness constraint for the interpolating solutions of the corresponding partial realization problem. In this paper, an alternative parameterization is developed for the solutions of the partial realization problems. Both the solutions of the partial and partial stochastic realization problem are analyzed in this parameterization, while the main concerns are the minimality and the uniqueness of the solutions. Based on the structure of the parameterization, a lower bound for the positive degree is derived. Kluwer Academic Publishers, 2000 rational covariance extension nationallicence minimal partial realization nationallicence partial stochastic realization nationallicence stochastic modeling nationallicence Van Gestel Tony Dept. of Electrical Engineering - ESAT/SISTA, K.U. Leuven, Kard. Mercierlaan 94, B-3001, Leuven, Belgium. e-mail aut Van Barel Marc Dept. of Computer Acience - NALAG, K. U. Leuven, Celestijnenlaan 200A, B-3001, Leuven, Belgium. e-mail aut De Moor Bart Dept. of Electrical Engineering -, ESAT/SISTA, K.U. Leuven, Kard. Mercierlaan 94, B-3001, Leuven, Belgium. e-mail aut Acta Applicandae Mathematica Kluwer Academic Publishers 61/1-3(2000-05-01), 317-331 0167-8019 61:1-3<317 2000 61 10440 https://doi.org/10.1023/A:1006405104724 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1006405104724 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Van Gestel Tony Dept. of Electrical Engineering - ESAT/SISTA, K.U. Leuven, Kard. Mercierlaan 94, B-3001, Leuven, Belgium. e-mail aut NATIONALLICENCE 700 1- Van Barel Marc Dept. of Computer Acience - NALAG, K. U. Leuven, Celestijnenlaan 200A, B-3001, Leuven, Belgium. e-mail aut NATIONALLICENCE 700 1- De Moor Bart Dept. of Electrical Engineering -, ESAT/SISTA, K.U. Leuven, Kard. Mercierlaan 94, B-3001, Leuven, Belgium. e-mail aut NATIONALLICENCE 773 0- Acta Applicandae Mathematica Kluwer Academic Publishers 61/1-3(2000-05-01), 317-331 0167-8019 61:1-3<317 2000 61 10440 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer