Differentiable structure of realizable Markov parameters |
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Authors: | I Baragaña F Puerta I Zaballa |
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Affiliation: | 1. Departamento de Ciencia de la Computación e IA. Universidad del País Vasco (UPV/EHU). Apdo. 649. 20080 Donostia-San Sebastián, Spain;2. Departament de Matemàtica Aplicada I. E.T.S. Enginyeria Industrial de Barcelona. UPC Institut d’Organització i Control(IOC) UPC Diagonal 647. 08028 Barcelona, Spain;3. Departamento de Matemática Aplicada y EIO. Universidad del País Vasco (UPV/EHU). Apdo. 644. 48080 Bilbao, Spain |
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Abstract: | The geometry of the finite sequences of p×m matrices that are realizable by systems of minimal order d is investigated. They can be stratified according to their partial row and column Kronecker indices. The case when the sum of the number of non-zero row and column indices is smaller than the number of elements in the sequence of parameters is considered. It is shown that, in this case, the whole set of Markov parameters and each stratum can be endowed with structures of differentiable manifolds, and their dimensions are computed. |
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Keywords: | Markov parameters Minimal realizations Controllability Observability Kronecker indices Transversality |
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