Locally positive nonlinear systems
International Journal of Applied Mathematics and Computer Science (2003)
- Volume: 13, Issue: 4, page 505-509
- ISSN: 1641-876X
Access Full Article
top
Abstract
topHow to cite
topKaczorek, Tadeusz. "Locally positive nonlinear systems." International Journal of Applied Mathematics and Computer Science 13.4 (2003): 505-509. <http://eudml.org/doc/207662>.
@article{Kaczorek2003,
abstract = {The notion of locally positive nonlinear time-varying linear systems is introduced. Necessary and sufficient conditions for the local positiveness of nonlinear time-varying systems are established. The concept of local reachability in the direction of a cone is introduced, and sufficient conditions for local reachability in the direction of a cone of this class of nonlinear systems are presented.},
author = {Kaczorek, Tadeusz},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {local reachability in the direction of a cone; nonlinear system; time-varying; local positiveness; time-varying nonlinear system; locally positive locally reachable linear approximation},
language = {eng},
number = {4},
pages = {505-509},
title = {Locally positive nonlinear systems},
url = {http://eudml.org/doc/207662},
volume = {13},
year = {2003},
}
TY - JOUR
AU - Kaczorek, Tadeusz
TI - Locally positive nonlinear systems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2003
VL - 13
IS - 4
SP - 505
EP - 509
AB - The notion of locally positive nonlinear time-varying linear systems is introduced. Necessary and sufficient conditions for the local positiveness of nonlinear time-varying systems are established. The concept of local reachability in the direction of a cone is introduced, and sufficient conditions for local reachability in the direction of a cone of this class of nonlinear systems are presented.
LA - eng
KW - local reachability in the direction of a cone; nonlinear system; time-varying; local positiveness; time-varying nonlinear system; locally positive locally reachable linear approximation
UR - http://eudml.org/doc/207662
ER -
References
top- d'Alessandro P. and de Santis E. (1994): Positivness of dynamic systems with non positive coefficients matrices. - IEEE Trans. Automat. Contr., Vol. AC-39, pp. 131-134.
- Berrman A., Neumann M. and Stern R. (1989): Nonnegative Matrices in Dynamic Systems. - New York: Wiley.
- Berman A. and Plemmons R.J. (1994): Nonnegative Matrices in Mathematical Sciences. - Philadelphia: SIAM Press. Zbl0815.15016
- Caccetta L. and Rumchev V.G. (1998): Reachable discrete-time positive systems with minimal dimension control sets. - Dynam. Cont. Discr. Impuls. Syst., Vol. 4, pp. 539-552. Zbl0927.93010
- Caccetta L. and Rumchev V.G. (2000): A survey of reachability and controllability for positive linear systems. - Ann. Opers. Res., Vol. 98, pp. 101-122. Zbl0972.93003
- Fanti M.P., Maione B. and Turchsano B. (1990): Controllability of multi-input positive discrete-time systems. - Int. J. Contr., Vol. 51, No. 6, pp. 1295-1308. Zbl0702.93012
- Farina L. and Rinaldi S. (2000): Positive Linear Systems, Theory and Applications.- New York: Wiley. Zbl0988.93002
- Fornasini E. and Valcher M.E. (1997): Recent developments in 2D positive systems theory. - J. Appl. Math. Comp. Sci., Vol. 7, No. 4, pp. 713-735. Zbl0913.93032
- Gantmacher F.R. (1959): The Theory of Matrices. - Chelsea, New York. Zbl0085.01001
- Kaczorek T. (2001): Externally and internally positive time-varying linear systems. - Int. J. Appl. Math. Comput. Sci., Vol. 11, No. 4, pp. 957-964. Zbl0997.93045
- Kaczorek T. (2002): Positive 1D and 2D Systems. -London: Springer-Verlag. Zbl1005.68175
- Kaczorek T. (1998): Weakly positive continuous-time linear systems. - Bull. Pol. Acad. Sci. Techn. Sci., Vol. 46, No. 2, pp. 233-245. Zbl0917.93048
- Kaczorek T. (1998): Positive descriptor discrete-time linear systems. - Probl. Nonlin. Anal. Eng. Syst., Vol. 1, No. 7, pp. 38-54.
- Klamka J. (1998): Constrained controllability of positive 2D systems. - Bull. Pol. Acad. Techn. Sci., Vol. 46, No. 1, pp. 93-102. Zbl1039.93003
- Klamka J. and Kalinowski J. (1998): Reachability and controllability of positive continuous-time linear systems with time variable coefficients. - Bull. Pol. Acad. Techn. Sci., Vol. 49, No. 4, pp. 633-641. Zbl0997.93009
- 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
- Rumchev V.G. (2000): Feedback and positive feedback holdability of discrete-time systems. - Syst. Sci., Vol. 26, No. 3, pp. 15-23. Zbl1068.93536
- Rumchev V.G. and Anstee R.P. (1999): Asymptotic reachable sets for discrete-time positive linear systems. - Syst. Sci., Vol. 25, No. 1, pp. 41-47. Zbl1068.93502
- 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
- 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
- Walczak S. (1984): A note on the controllability of nonlinear systems. - Math. Syst. Theory, Vol. 17, pp. 351-356. Zbl0628.93005
- 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
- Valcher M.E. (1997): On the internal stability and asymptotic behaviour of 2D positive systems. - IEEE Trans. Circ. Syst., Part I, Vol. 44, pp. 602-613. Zbl0891.93046
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.