# Monomial subdigraphs of reachable and controllable positive discrete-time systems

Rafael Bru; Louis Caccetta; Ventsi Rumchev

International Journal of Applied Mathematics and Computer Science (2005)

- Volume: 15, Issue: 1, page 159-166
- ISSN: 1641-876X

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topBru, Rafael, Caccetta, Louis, and Rumchev, Ventsi. "Monomial subdigraphs of reachable and controllable positive discrete-time systems." International Journal of Applied Mathematics and Computer Science 15.1 (2005): 159-166. <http://eudml.org/doc/207724>.

@article{Bru2005,

abstract = {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.},

author = {Bru, Rafael, Caccetta, Louis, Rumchev, Ventsi},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {positive linear systems; monomial subdigraphs; reachability; controllability; system structure},

language = {eng},

number = {1},

pages = {159-166},

title = {Monomial subdigraphs of reachable and controllable positive discrete-time systems},

url = {http://eudml.org/doc/207724},

volume = {15},

year = {2005},

}

TY - JOUR

AU - Bru, Rafael

AU - Caccetta, Louis

AU - Rumchev, Ventsi

TI - Monomial subdigraphs of reachable and controllable positive discrete-time systems

JO - International Journal of Applied Mathematics and Computer Science

PY - 2005

VL - 15

IS - 1

SP - 159

EP - 166

AB - 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.

LA - eng

KW - positive linear systems; monomial subdigraphs; reachability; controllability; system structure

UR - http://eudml.org/doc/207724

ER -

## References

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- Coxson P.G., Larson I.C. and Schneider H.(1987): Monomial patterns in the sequence A^{k}b - Lin. Alg. Applic., Vol. 94, pp. 89-101. Zbl0649.15009
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- Kaczorek T. (2002): Positive 1D and 2D Systems. - Heidelberg: Springer. Zbl1005.68175
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- Rumchev V.G. (2000): On controllability of discrete-time positive systems. - Proc. 6-th Int. Conf. Contr. Automat., Robot. and Vision, Singapore, pp. 1923-1927, (on CD-ROM).
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