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Języki publikacji
Abstrakty
In this paper necessary and sufficient conditions (and criteria) for null-controllability, reachability and controllability of time-variant discrete-time positive linear systems are established. These properties appear to be entirely structural properties, that is, they do depend on the zero-nonzero pattern of the pair (A(k), B[k)) > 0 and do not depend on the values of its entries. An interesting phenomenon has been revealed namely the time needed to reach the origin for a null-controllable system as well as the time to reach a (non-negative) state from the origin for a reachable system can be less, equal or greater than the dimension of the system. This phenomenon has no equivalent in the case of time-invariant discrete-time positive linear systems where this time is always less or equal to the system dimension. Examples are provided.
Czasopismo
Rocznik
Tom
Strony
85--94
Opis fizyczny
Bibliogr. 11 poz.
Twórcy
autor
- Department of Mathematics and Statistics Curtin University of Technology GPO Box U 1987, Perth, WA 6845, Australia
autor
- Department of Electrical and Computer Engineering
Bibliografia
- Bru, R. and Johnson, C. R. (1993) Nilpotence of products of nonnegative matrices. Rocky Mountain Journal of Mathematics 23(1), 5-16.
- Bru R., Coll C., Romero-Vivo,and Sanchez E. (2003) Some problems about structural properties of positive descriptor systems. In: L. Benvenuti et al., eds., Positive Systems. Lecture Notes in Control and Information Sciences 294, Springer-Verlag, Berlin, 233-240.
- Caccetta, L. and Rumchev, V. G. (2000) A survey of reachability and controllability for positive linear systems. Annals of Operations Research 98,101-122.
- Coxson, P. G., Larson, L.C. and Schneider, H. (1987) Monomial patterns in the sequence Akb. Linear Algebra and its Applications 94, 89-101.
- Farina, L. and Rinaldi, S. (2000) Positive Linear Systems: Theory and Applications. John Wiley & Sons, New York.
- Kaczorek, T. (2001) Externally and internally positive time-varying linear systems. Intern. Journal of Applied Math. and Comp. Sci.11(4),957-964.
- Kaczorek, T. (2002) Positive 1D and 2D Systems. Springer, London.
- Klamka J. (2002) Positive controllability of positive dynamical systems. Proc. American Control Conference ACC 2002, IEEE Catalog Number: 02CH37301C, May 8-10, Anchorage, Alaska, USA, 4632-4637.
- Luenberger, D.G. (1979) Introduction to Dynamic Systems: Theory, Modelsand Applications. Academic Press, New York.
- Rumchev, V. and James, D.G. (1989) Controllability of positive linear discrete-time systems. International Journal of Control 50(3), 845-857.
- Rumchev V. (2003) Positive linear systems reachability criterion in digraphform. In: L. Benvenuti et al., eds., Positive Systems. Lecture Notes in Control and Information Sciences 294, Springer-Verlag, Berlin, 241-248.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0007-0043