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51. An Algorithm for the Single-Input Pole Assignment Problem

Author

Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada, Bru, Rafael, Mas Marí, José, Urbano Salvador, Ana María, Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada, Bru, Rafael, Mas Marí, José, and Urbano Salvador, Ana María

Abstract

[EN] B. N. Datta and K. Datta have proposed an efficient parallel algorithm for the single-input pole assignment problem when the spectrum set to be assigned is pairwise distinct and disjoint from the spectrum of the dynamical matrix. This paper first presents a theoretical analysis of that algorithm and then presents the necessary modifications on it for an arbitrary spectrum. Based on the modified algorithm, the authors present two new algorithms for the problem and give some results on controllability that are of independent interests.

Published
1994

66. A Brauer's theorem and related results.

Author

Bru, Rafael, Cantó, Rafael, Soto, Ricardo, and Urbano, Ana

Abstract

Given a square matrix A, a Brauer's theorem [Brauer A., Limits for the characteristic roots of a matrix. IV. Applications to stochastic matrices, Duke Math. J., 1952, 19(1), 75-91] shows how to modify one single eigenvalue of A via a rank-one perturbation without changing any of the remaining eigenvalues. Older and newer results can be considered in the framework of the above theorem. In this paper, we present its application to stabilization of control systems, including the case when the system is noncontrollable. Other applications presented are related to the Jordan form of A and Wielandt's and Hotelling's deflations. An extension of the aforementioned Brauer's result, Rado's theorem, shows how to modify r eigenvalues of A at the same time via a rank- r perturbation without changing any of the remaining eigenvalues. The same results considered by blocks can be put into the block version framework of the above theorem. [ABSTRACT FROM AUTHOR]

Published
2012
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69. On M–multisplittings of singular M–matrices with application to Markov chains.

Author

Bru, Rafael, Cantó, Rafael, and Climent, Joan-Josep

Subjects
*MATRICES (Mathematics), *MARKOV processes, *LINEAR systems, *STOCHASTIC convergence, *ITERATIVE methods (Mathematics), *BOUNDARY value problems
Abstract

Given a singular M–matrix of a linear system, convergent conditions under which iterative schemes based on M–multisplittings are studied. Two of those conditions, the index of the iteration matrix and its spectral radius are investigated and related to those of the M-matrix. Furthermore, a parallel multisplitting iteration scheme for solving singular linear systems is suggested which can be applied to practical problems such as Poisson and elasticity problems under certain boundary conditions, the Neumann problem, and in Markov chains. A discussion of that multisplitting scheme, based on Gauss–Seidel type splittings is given for computing the stationary distribution vector of Markov chains. In this case a computational viable algorithm can be constructed, since only the nonsingularity of one weighting matrix of the multisplitting is needed. © 1998 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Published
1998
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70. Structural properties of discrete-time linear positive periodic systems

Author

Bru, Rafael and Hernández, Vicente

Abstract

We study reachability and controllability properties for discrete-time positive periodic systems. The equivalence between N-periodic systems, with nstates and minputs, and invariant systems, with nstates and Nminputs, preserves the positivity of such systems, and in addition, closely relates their reachability cones. This equivalence permits us to show that the complete contrallability (reachability) of a positive N-periodic system is equivalent to the complete contrallability (reachability) of Nassociated positive invariant systems.

Published
1989
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72. Generalized Bezoutian for Discrete-Time Linear Periodic Systems

Author

Coll, Carmen, Bru, Rafael, and Heranández, Vicente

Abstract

We introduce the concept of periodic generalized Bezoutians associated to a discrete-time linear periodic systems or periodic rational matrices. Given a collection of periodic rational matricest we characterize the dimension of minimal realizations by means of the rank of the periodic generalized Bezoutian matrix.

Published
1992
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73. El tesoro como objeto de derechos reales

Author

Montes Bru, Rafael, García-Valdecasas, and Universidad de Granada.Departamento de Derecho Civil

Subjects
347.2, Derechos reales, Tesis doctorales
Abstract

Reducción alta, Univ. de Granada, Departamento de Derecho Civil. Leída el 09-12-80, Posibilidad de constituir sobre el tesoro un derecho real independiente del bien que lo contiene. Bien sea un derecho real atípico o una servidumbre personal de acuerdo con el numerus apertus que impera en nuestro derecho y del principio de autonomía de la voluntad. Así como otras materias relacionadas con el tesoro.

Published
1989

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