Externally and internally positive time-varying linear systems
Kaczorek, Tadeusz
International Journal of Applied Mathematics and Computer Science, Tome 11 (2001), p. 957-964 / Harvested from The Polish Digital Mathematics Library

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.

Publié le : 2001-01-01
EUDML-ID : urn:eudml:doc:207539
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     author = {Kaczorek, Tadeusz},
     title = {Externally and internally positive time-varying linear systems},
     journal = {International Journal of Applied Mathematics and Computer Science},
     volume = {11},
     year = {2001},
     pages = {957-964},
     zbl = {0997.93045},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv11i4p957bwm}
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Kaczorek, Tadeusz. Externally and internally positive time-varying linear systems. International Journal of Applied Mathematics and Computer Science, Tome 11 (2001) pp. 957-964. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv11i4p957bwm/

[000] d'Alessandro P. and de Santis E. (1994): Positiveness of dynamic systems with non-positive coefficients matrices. — IEEE Trans. Automat. Contr., Vol.AC-39, pp.131–134.

[001] Berrman A., Neumann M. and Stern R. (1989): Nonnegative Matrices in Dynamic Systems. — New York: Wiley.

[002] Berman A. and Plemmons R.J. (1994): Nonnegative Matrices in Mathematical Sciences. — Philadelphia: SIAM Press. | Zbl 0815.15016

[003] 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. | Zbl 0702.93012

[004] Farina L. and Rinaldi S. (2000): Positive Linear Systems, Theory and Applications. — New York: Wiley. | Zbl 0988.93002

[005] Fornasini E. and Valcher M.E. (1997): Recent developments in 2D positive systems theory. — J. App. Math. Comp. Sci., Vol.7, No.4, pp.101–123. | Zbl 0913.93032

[006] Gantmacher F.R. (1959): The Theory of Matrices. — New York: Chelsea. | Zbl 0085.01001

[007] Kaczorek T. (1998a): Weakly positive continuous-time linear systems. — Bull. Pol. Acad. Techn. Sci., Vol.46, No.2, pp.233–245. | Zbl 0917.93048

[008] Kaczorek T. (1998b): Positive descriptor discrete-time linear systems. — Prob. Nonlin. Anal. Eng. Syst., Vol.1, No.7, pp.38–54.

[009] Kaczorek T. (2001): Positive 1D and 2D Systems. — London: Springer. | Zbl 1005.68175

[010] Klamka J. (1998): Constrained controllability of positive 2D systems. — Bull. Pol. Acad. Techn. Sci., Vol.46, No.1, pp.93–102. | Zbl 1039.93003

[011] 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. | Zbl 0539.93005

[012] 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).

[013] 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. | Zbl 0717.93039

[014] 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. | Zbl 0818.93027

[015] Valcher M.E. (1996): Controllability and reachability criteria for discrete-time positive systems. — Int. J. Contr., Vol.65, No.3, pp.511–536. | Zbl 0873.93009

[016] 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. | Zbl 0891.93046