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Monomial subdigraphs of reachable and controllable positive discrete-time systems

100%
Bru R., Caccetta L., Rumchev V. G.
International Journal of Applied Mathematics and Computer Science
|
2005
|
tom 15
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nr 1
159-166
EN
A generic structure of reachable and controllable positive linear systems is given in terms of some characteristic components (monomial subdigraphs) of the digraph of a non-negative a pair. The properties of monomial subdigraphs are examined and used to derive reachability and controllability criteria in a digraph form for the general case when the system matrix may contain zero columns. The graph-theoretic nature of these criteria makes them computationally more efficient than their known equivalents. The criteria identify not only the reachability and controllability properties of positive linear systems, but also their reachable and controllable parts (subsystems) when the system does not possess such properties.
2
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Characterization of α1 and α2-matrices

100%
Bru R., Cvetković L., Kostić V., Pedroche F.
Open Mathematics
|
2010
|
tom 8
|
nr 1
32-40
EN
This paper deals with some properties of α1-matrices and α2-matrices which are subclasses of nonsingular H-matrices. In particular, new characterizations of these two subclasses are given, and then used for proving algebraic properties related to subdirect sums and Hadamard products.
3
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A Brauer’s theorem and related results

100%
Bru R., Cantó R., Soto R., Urbano A.
Open Mathematics
|
2012
|
tom 10
|
nr 1
312-321
EN
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.
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