Externally and internally positive time-varying linear systems

Tadeusz Kaczorek

International Journal of Applied Mathematics and Computer Science (2001)

  • Volume: 11, Issue: 4, page 957-964
  • ISSN: 1641-876X

Abstract

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The notions of externally and internally positive time-varying linear systems are introduced. Necessary and sufficient conditions for the external and internal positivities of time-varying linear systems are established. Moreover, sufficient conditions for the reachability of internally positive time-varying linear systems are presented.

How to cite

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Kaczorek, Tadeusz. "Externally and internally positive time-varying linear systems." International Journal of Applied Mathematics and Computer Science 11.4 (2001): 957-964. <http://eudml.org/doc/207539>.

@article{Kaczorek2001,
abstract = {The notions of externally and internally positive time-varying linear systems are introduced. Necessary and sufficient conditions for the external and internal positivities of time-varying linear systems are established. Moreover, sufficient conditions for the reachability of internally positive time-varying linear systems are presented.},
author = {Kaczorek, Tadeusz},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {None; nonnegative systems; internally positive time-varying linear systems; reachability},
language = {eng},
number = {4},
pages = {957-964},
title = {Externally and internally positive time-varying linear systems},
url = {http://eudml.org/doc/207539},
volume = {11},
year = {2001},
}

TY - JOUR
AU - Kaczorek, Tadeusz
TI - Externally and internally positive time-varying linear systems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2001
VL - 11
IS - 4
SP - 957
EP - 964
AB - The notions of externally and internally positive time-varying linear systems are introduced. Necessary and sufficient conditions for the external and internal positivities of time-varying linear systems are established. Moreover, sufficient conditions for the reachability of internally positive time-varying linear systems are presented.
LA - eng
KW - None; nonnegative systems; internally positive time-varying linear systems; reachability
UR - http://eudml.org/doc/207539
ER -

References

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  9. Kaczorek T. (1998b): Positive descriptor discrete-time linear systems. — Prob. Nonlin. Anal. Eng. Syst., Vol.1, No.7, pp.38–54. 
  10. Kaczorek T. (2001): Positive 1D and 2D Systems. — London: Springer. Zbl1005.68175
  11. Klamka J. (1998): Constrained controllability of positive 2D systems. — Bull. Pol. Acad. Techn. Sci., Vol.46, No.1, pp.93–102. Zbl1039.93003
  12. Ohta Y., Madea H. and Kodama S. (1984): Reachability, observability and realizability of continuous-time positive systems. — SIAM J. Contr. Optim., Vol.22, No.2, pp.171–180. Zbl0539.93005
  13. Ratajczak Z. (1967): On solutions of the system of homogenous differential linear equations. — Scientific Fasicicles of Poznań University of Technology, Mathematics, No.3 pp.59– 64 (in Polish). 
  14. Rumchev V.G. and James D.J.G. (1990): The role of nonnegative matrices in discrete-time mathematical modelling. — Int. J. Math. Educ. Sci. Technol., Vol.21, No.2, pp.169–182. Zbl0717.93039
  15. Rumchev V.G. and James D.J.G. (1995): Spectral characterisation and pole assignment for positive linear discrete-time systems. — Int. J. Syst. Sci., Vol.26, No.2, pp.295–312. Zbl0818.93027
  16. Valcher M.E. (1996): Controllability and reachability criteria for discrete-time positive systems. — Int. J. Contr., Vol.65, No.3, pp.511–536. Zbl0873.93009
  17. Valcher M.E. (1997): On the internal stability and asymptotic behaviour of 2D positive systems, Part I. — IEEE Trans. Circ. Syst., Vol.44, No.7, pp.602–613. Zbl0891.93046

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