Tytuł artykułu
Treść / Zawartość
Pełne teksty:
Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
Positive state controllability is the controllability of systems where the state is positive and the input remains in ℝn. Under some conditions, we established a relation between the reachability map of systems with only the positive state and the reachability map of a related positive system where the state and input are both positive. Using this connection, necessary and sufficient conditions are obtained for the positive state reachability of discrete linear time-invariant (LTI) systems, and then we deduced the positive state controllability. These conditions are evaluated over some numerical examples that support the theoretical results.
Czasopismo
Rocznik
Tom
Strony
110--118
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
autor
- Faculty of Sciences, Department of Mathematics, Chouaib Doukkali University, BP.20, 24000 El Jadida, Morocco
autor
- Faculty of Sciences, Department of Mathematics, Chouaib Doukkali University, BP.20, 24000 El Jadida, Morocco
autor
- Faculty of Sciences, Department of Mathematics, Chouaib Doukkali University, BP.20, 24000 El Jadida, Morocco
Bibliografia
- 1. Bartholomew DJ, Forbes AF, McLean SI. Statistical techniques for manpower planning. 2nd ed, Wiley, New York. 1979.
- 2. Berman A, Neumann M, Stern RJ. Nonnegative matrices in dynamic systems. Vol. 3. Wiley-Interscience. 1989.
- 3. Brown RF. Biomedical systems analysis via compartmental concept. CRC Press; 1985.
- 4. Caccetta L, Rumchev VG. A survey of reachability and controllability for positive linear systems. Annals of Operations Research. 2000:101-22.
- 5. Cáceres MO, Cáceres-Saez I. Random Leslie matrices in population dynamics. Journal of Mathematical Biology. 2011;63:519-56.
- 6. Chase RB, Aquilano NJ. Production and Operations Management, Richard D. Irwin, Chicago, IL. 1992.
- 7. Coxson PG, Shapiro H. Positive input reachability and controllability of positive systems. Linear Algebra and its Applications. 1987:1;94:35-53.
- 8. Doak D, Kareiva P, Klepetka B. Modeling population viability for the desert tortoise in the western Mojave Desert. Ecological applications. 1994 Aug;4(3):446-60.
- 9. Farina L, Rinaldi S. Positive linear systems: theory and applications. John Wiley & Sons; 2000 Jul 3.
- 10. Guiver C, Hodgson D, Townley S. Positive state controllability of positive linear systems. Systems & Control Letters. 2014:1;65: 23-9.
- 11. Kalman RE, Ho YC, Narendra KS. Controllability of linear dynamical systems. In Contributions to Differential Equations. 1962;1: 189–213.
- 12. Kaczorek T. Positive 1D and 2D systems. Springer Science & Busi-ness Media; 2012 Dec 6.
- 13. Krasnoselskii MA, Lifshitz EA, Sobolev AV. Positive Linear Systems, Nauka, Moscow, in Russian. 1985.
- 14. Lubben J, Tenhumberg B, Tyre A, Rebarber R. Management rec-ommendations based on matrix projection models: the importance of considering biological limits. Biological Conservation. 2008; 1;141(2):517-23.
- 15. Luenberger DG. Theory, models and applications. Stanford Universi-ty. John Wiley & Sons Inc; 1979.
- 16. Ouyadri M, Laabissi M, Achhab ME. Positive output controllability of linear discrete–time invariant systems. Control and Cybernetics. 2021 Oct 1;50(4):521-39.
- 17. Rantzer A, Valcher ME. A tutorial on positive systems and large scale control. In 2018 IEEE Conference on Decision and Control (CDC). 2018:3686-3697.
- 18. Rumchev VG, Konin AL. Decision support systems for manpower planning: Mathematical Models. Radio and Communication Press, Moscow. 1984.
- 19. Sethi SP, Thompson GL. Optimal Control Theory: Applications to Management Sciences. Martinus Nijhoff, Boston. 1981.
- 20. Szidarovszky F. Linear systems theory. Routledge; 2018.
- 21. Valcher ME. Controllability and reachability criteria for discrete time positive systems. International Journal of Control. 1996:1;65(3): 511-36.
- 22. Vollmann TE, Berry WL, Whybark DC. Manufacturing planning and control systems. Irwin/McGraw-Hill. 1997.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-df5bf72e-40fe-4523-8d8b-029ecc7438a0