Externally and internally positive singular discrete-time linear systems

Tadeusz Kaczorek

International Journal of Applied Mathematics and Computer Science (2002)

  • Volume: 12, Issue: 2, page 197-202
  • ISSN: 1641-876X

Abstract

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Notions of externally and internally positive singular discrete-time linear systems are introduced. It is shown that a singular discrete-time linear system is externally positive if and only if its impulse response matrix is non-negative. Sufficient conditions are established under which a single-output singular discrete-time system with matrices in canonical forms is internally positive. It is shown that if a singular system is weakly positive (all matrices E, A, B, C are non-negative), then it is not internally positive.

How to cite

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Kaczorek, Tadeusz. "Externally and internally positive singular discrete-time linear systems." International Journal of Applied Mathematics and Computer Science 12.2 (2002): 197-202. <http://eudml.org/doc/207579>.

@article{Kaczorek2002,
abstract = {Notions of externally and internally positive singular discrete-time linear systems are introduced. It is shown that a singular discrete-time linear system is externally positive if and only if its impulse response matrix is non-negative. Sufficient conditions are established under which a single-output singular discrete-time system with matrices in canonical forms is internally positive. It is shown that if a singular system is weakly positive (all matrices E, A, B, C are non-negative), then it is not internally positive.},
author = {Kaczorek, Tadeusz},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {singular; positive; internally; externally; system; linear; linear systems},
language = {eng},
number = {2},
pages = {197-202},
title = {Externally and internally positive singular discrete-time linear systems},
url = {http://eudml.org/doc/207579},
volume = {12},
year = {2002},
}

TY - JOUR
AU - Kaczorek, Tadeusz
TI - Externally and internally positive singular discrete-time linear systems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2002
VL - 12
IS - 2
SP - 197
EP - 202
AB - Notions of externally and internally positive singular discrete-time linear systems are introduced. It is shown that a singular discrete-time linear system is externally positive if and only if its impulse response matrix is non-negative. Sufficient conditions are established under which a single-output singular discrete-time system with matrices in canonical forms is internally positive. It is shown that if a singular system is weakly positive (all matrices E, A, B, C are non-negative), then it is not internally positive.
LA - eng
KW - singular; positive; internally; externally; system; linear; linear systems
UR - http://eudml.org/doc/207579
ER -

References

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  12. Luenberger D.G. (1978): Time-invariant descriptor systems. - Automatica, Vol. 14, No.2, pp. 473-480. Zbl0398.93040
  13. Mertzios B.G. and Lewis F.L. (1989): Fundamental matrix of discrete singular systems.-Circuits Syst. Signal Process., Vol. 8, No. 3, pp. 341-355. Zbl0689.93041
  14. 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

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