RESEARCH PAPER
Positive State Controllability of Discrete Linear Time-Invariant Systems
1
Faculty of Sciences, Department of Mathematics, Chouaib Doukkali University, BP.20, 24000 El Jadida, Morocco
Submission date: 2023-04-26
Acceptance date: 2023-08-08
Online publication date: 2024-02-29
Publication date: 2024-03-01
Acta Mechanica et Automatica 2024;18(1):110-118
KEYWORDS
ABSTRACT
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.
REFERENCES (22)
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.
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 & Business 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 recommendations 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 University. 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.
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.
| eISSN: | 2300-5319 |
| ISSN: | 1898-4088 |
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