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Stability of positive linear discrete-time systems

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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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  • Control Theory and Applications Centre, Coventry University, Priory Street, Coventry, CV1 5FB, UK., g.james@coventry.ac.uk
Bibliografia
  • [1] D.J.G. James and V.G. Rumchev, “Cohort-type models and their reachability and controllability properties”, Systems Science 26, 43–54 (2000).
  • [2] D.J.G. James and V.G.Rumchev, “Reachability and controllability of compartmental systems”, Systems Science 26, 5–13 (2000).
  • [3] D.J.G. James and V.G. Rumchev, “A fractional-flow model of serial manufacturing systems with rework and its reachability and controllability properties”, Systems Science 27, 49–59 (2001).
  • [4] D.J.G. James and V.G. Rumchev, “Controlled balanced growth of robot population”, Proceedings 9th International Symposium on Artificial Life and Robotics, (ed: M. Sugisaka and H. Tanaka), Beppu, Japan, 2, 622–628 (2004).
  • [5] D.G. Luenberger, Introduction to Dynamical Systems, Wiley, New York, 1979.
  • [6] V.G. Rumchev, L. Caccetta and S. Kostova, “Positive linear dynamic model of mobile source of pollution and problems of control”, Proceedings of 16th International Conference Systems Engineering, (ed: K.J. Burnham and O.C.L. Haas), Coventry University, Coventry 2, 602–607 (2003).
  • [7] V.G. Rumchev and D.J.G. James, “The role of nonnegative matrices in discrete-time mathematical modeling”, International Journal Mathematical Education in Science and Technology 21, 161–182 (1990).
  • [8] H. Minc, Non-negative Matrices, John Wiley & Sons, NY, 1988.
  • [9] L. Farina and S. Rinaldi, Positive Linear Systems – Theory and Applications, John Wiley & Sons, NY, 2000.
  • [10] T. Kaczorek, Positive 1D and 2D Systems, Springer, London, 2002.
  • [11] A. Graham, Non-negative Matrices and Applicable Topics in Linear Algebra, Ellis Horwood, Chichester, UK, 1988.
  • [12] A. Berman and R. Plemmons, Non-negative Matrices in the Mathematical Sciences, SIAM: Classics in Applied Mathematics, Philadelphia, 1994.
  • [13] H. Wieland, “Unzerlegbare nicht negtiven matrizen”, Mathematisce Zeitschrift 52, 642–648 (1950).
  • [14] V.G. Rumchev and D.J.G. James, “Controllability of positive linear discrete-time systems”, International Journal of Control 50, 45–857 (1989).
  • [15] S. Muratori and S. Rinaldi, “Excitability, stability and sign of the equilibria in positive linear systems”, Systems and Control Letters 16, 59–63 (1991).
  • [16] V.G. Rumchev and D.J.G. James, “Spectral characterization of pole-assignment for positive linear discrete-time systems”, International Journal of Systems Science 16, 295–312 (1995).
  • [17] R.A. Horn and C.A. Johnson, Matrix Analysis, Cambridge Press, Cambridge, UK 1985.
  • [18] R. Bhatia, L. Elsner and G. Krause, “Bounds for the variation of the roots of a polynomial and eigenvalues of a matrix”, Linear Algebra and its Applications 142, 195–209 (1990).
  • [19] M. Haviv, Y. Ritov and U.G. Rothblum, “Iterative methods for approximating the subdominant modulus of an eigenvalue of a nonnegative matrix”, Linear Algebra and its Applications 87, 61–75 (1987).
  • [20] T.S. Leong, “A note on upper bounds on the maximum modulus of subdominant eigenvalues of nonnegative matrices”, Linear Algebra and its Applications 106, 1–4 (1988).
  • [21] H. Wolkowicz and G.P.H. Styan, “Bounds for eigenvalues using traces”, Linear Algebra and its Applications 29, 471–506 (1980).
  • [22] V.G. Rumchev and J. Adeane, “Reachability and controllability of discrete-time positive linear systems”, Control and Cybernetics 33, 85–94 (2004).
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Bibliografia
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bwmeta1.element.baztech-article-BPG5-0005-0042
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