Coxson, Pamela G.; Shapiro, Helene Positive input reachability and controllability of positive systems. (English) Zbl 0633.93008 Linear Algebra Appl. 94, 35-53 (1987). Controllability and reachability for linear discrete finite-dimensional time-invariant control systems are studied. It is assumed that the systems are positive, i.e., all parameters are nonnegative and the controls are also nonnegative. For such positive systems several conditions for various kinds of controllability and reachability are presented and proved. The relations to unconstrained controllability problems are given and explained. Some illustrative examples are also presented. Moreover, general remarks and comments on constrained controllability are given. Similar problems have been recently considered in a paper by D. N. P. Murthy [Int. J. Syst. Sci. 17, 49-54 (1986; Zbl 0581.93010)]. Reviewer: J.Klamka Cited in 1 ReviewCited in 39 Documents MSC: 93B05 Controllability 93C05 Linear systems in control theory 93C55 Discrete-time control/observation systems 93B03 Attainable sets, reachability Keywords:attainable sets; Controllability; reachability; linear discrete finite- dimensional time-invariant control systems; positive systems; time-invariant Citations:Zbl 0581.93010 PDFBibTeX XMLCite \textit{P. G. Coxson} and \textit{H. Shapiro}, Linear Algebra Appl. 94, 35--53 (1987; Zbl 0633.93008) Full Text: DOI References: [1] Bacciotti, A., On the positive orthant controllability of two dimensional bilinear systems, Systems and Control Lett., 3, 1, 53-55 (1983) · Zbl 0532.93005 [2] Berman, A.; Plemmons, R. J., Nonnegative Matrices in the Mathematical Sciences (1979), Academic: Academic New York · Zbl 0484.15016 [3] Boothby, W., Some comments on positive orthant controllability of bilinear systems, SIAM J. Control Optim., 20, 5, 634-644 (1982) · Zbl 0488.93009 [4] Coxson, P. G.; Larson, L. C.; Schneider, H., Monomial patterns in the sequence \(A^kb\), Linear Algebra Appl., 94, 89-101 (1987) · Zbl 0649.15009 [5] Gantmacher, F. R., The Theory of Matrices, Vols. 2 (1964), Chelsea>: Chelsea> New York · Zbl 0085.01001 [6] Goldstein, A.; Aronow, W.; Kalman, S., Principles of Drug Action: The Basis of Pharmacology (1974), Wiley: Wiley New York [7] Luenberger, D. G., Introduction to Dynamic Systems (1979), Wiley: Wiley New York · Zbl 0458.93001 [8] Maeda, H.; Kodama, S., Positive realization of difference equations, IEEE Trans. Circuits and Systems, CAS-28, 1, 39-47 (1981) · Zbl 0469.93035 [9] Nieuwenhuis, J. W., About nonnegative realizations, Systems and Control Lett., 1, 5, 238-287 (1982) · Zbl 0484.93018 [10] Ohta, Y.; Maeda, H.; Kodama, S., Reachability, observability and realizability of continuous-time positive systems, SIAM J. Control Optim., 22, 2, 171-180 (1984) · Zbl 0539.93005 [11] Murthy, D. N.P., Controllability of a linear positive dynamic system, Int. J. Systems Sci., 17, 1, 49-54 (1986) · Zbl 0581.93010 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.