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Stability of positive linear discrete-time systems

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EN
Abstrakty
EN
The main focus of the paper is on the asymptotic behaviour of linear discrete-time positive systems. Emphasis is on highlighting the relationship between asymptotic stability and the structure of the system, and to expose the relationship between null-controllability and asymptotic stability. Results are presented for both time-invariant and time-variant systems.
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Strony
51--67
Opis fizyczny
Bibliogr. 22 poz.,
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autor
Bibliografia
  • [1] Bhatia R., Elsner L., Krause G., Bounds for the variation of the roots of a polynomial and eigen values of a matrix. Linear algebra and its applications, Vol. 142, 1990, 195-209.
  • [2] Caccetta L., Rumchev V., Survey of reachability and controllability for positive linear systems, Annals of Operations Research, Vol. 98, 2000, 101-122.
  • [3] Farina L., Rinaldi S., Positive Linear Systems - Theory and Applications, John Wiley & Sons NY 2000.
  • [4] Graham A., Non-negative matrices and applicable topics in linear algebra, Ellis Horwood Chichester, UK, 1988.
  • [5] Haviv M., Ritov Y., Rothblum U. G., Iterative methods for approximating the subdominan modulus of an eigenvalue of a nonnegative matrix. Linear algebra and its applications Vol 87 1987,61-75.
  • [6] Horn R. A., Johnson C. A., Matrix Analysis, Cambridge Press, Cambridge, UK 1985.
  • [7] James D. J. G., Rumchev V. G., Cohort-type models and their reachability and controllability properties. Systems Science, Vol. 26, No. 2, 2000, 43-54.
  • [8] James D. J. G., Rumchev V. G., Reachability and controllability of compartmental systems. Systems Science, Vol. 26, No. 1, 2000, 5-13.
  • [9] James G., Rumchev V., A fractional-flow model of serial manufacturing systems with rework ad its reachability and controllability properties. Systems Science, Vol. 27, No. 2, 2001, 49-59.
  • [10] James D. J. G., Rumchev V. G., Controlled balanced growth of robot population. Proceedings 9th International Symposium on Artificial Life and Robotics, (Eds.: Sugisaka M., Tanaka H.), Vol. 2, Beppu, Japan, 2004, 622-628.
  • [11] Kaczorek T., Positive ID and 2D Systems, Springer, London, 2002.
  • [12] Leong T. S., a note on upper bounds on the maximum modulus of subdominant eigenvalues of nonnegative matrices. Linear algebra and its applications. Vol. 106, 1988, 1-4
  • [13] Luenberger D. G., Introduction to Dynamical Systems, Wiley, New York 1979.
  • [14] Minc H., Non-negative Matrices, John Wiley & Sons, NY, 1988.
  • [15] Muratori S., Rinaldi S., Excitability, stability and sign of the equilibria in positive linear systems, Systems and Control Letters, Vol. 16, 1991, 59-63.
  • [16] Rumchev V., Adeane J., Reachability and controllability of discrete-time positive linear systems, Control and Cybernetics, Vol. 33, No. 1, 2004, (in press).
  • [17] Rumchev V., Caccetta L., Kostova S., Positive linear dynamic model of mobile source of pollution and problems of control. Proceedings of 16th International Conference Systems Engineering (Eds.: Bumham K. J., Haas O. C. L.), Vol. 2, Coventry University, Coventry 2003, 602-607.
  • [18] Rumchev V., James D. J. G., Controllability of positive linear discrete-time systems. International Journal of Control, Vol. 50, No. 3, 1989, 45-57.
  • [19] Rumchev V. G., James D. J. G., The role of non-negative matrices in discrete-time mathematical modeling. International Journal Mathematical Education in Science an Technolgy, Vol. 21, No. 2, 1990, 161-182
  • [20] Rumchev V., . James D. J. G., Spectral characterization of pole-assignment for positive linear discrete-time systems, International journal of Systems Science. Vol 16, No. 2, 1995, 295-312
  • [21] Wieland H., Unzerlegbare nicht negtiven Matriez, , Mathematisce Zeitschrift, Vol. 52, 1950 642-648
  • [22] Wolkiewicz H., Stygan G. H., Bounds for eigenvalues using traces. Linear algebra and its applications, Vol. 29, 1980 471-506
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0008-0036
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