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

Abstract

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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.

How to cite

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Bru, 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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  1. Bru R., Romero S. and Sánchez E.(2000): Canonical forms for positive discrete-time linear control systems. - Lin. Alg. Appl., Vol. 310, pp. 49-71. Zbl0968.93016
  2. Caccetta L. and Rumchev V.G.(1998): Reachable discrete-time positive systems with minimal dimension control sets. - Dyn. Cont. Discr. Imp. Syst.,Vol. 4, No. 4, pp. 539-552. Zbl0927.93010
  3. 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
  4. Coxson P.G. and Shapiro H.(1987): Positive input reachability and controllability of positive systems. - Lin. Alg. Applic., Vol. 94, pp. 35-53. Zbl0633.93008
  5. Kaczorek T. (2002): Positive 1D and 2D Systems. - Heidelberg: Springer. Zbl1005.68175
  6. Lin C.T. (1974): Structural controllability. - IEEE Trans. Automat. Contr., Vol. AC-19, No. 3, pp. 201-208. Zbl0282.93011
  7. Muratori S. and Rinaldi S.(1991): Excitability,stability, and sign of equilibria in positive linear systems. - Syst. Contr. Lett., Vol. 16, pp. 59-63. Zbl0733.93029
  8. Murthy D.N.P.(1986): Controllability of a linear positive dynamic system. - Int. J. Syst. Sci., Vol. 17, No. 1, pp. 49-54. Zbl0581.93010
  9. 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). 
  10. Rumchev V.G. and James D.J.G.(1989): Controllability of positive discrete-time systems. - Int. J. Contr., Vol. 50, No. 3, pp. 845-857. Zbl0695.93009

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