Stability of positive linear discrete-time systems

Bulletin of the Polish Academy of Sciences, Technical Sciences

Volumn 53, Issue 1, 2005, Pages 1-8

  James, G ^a   Rumchev, V ^b  

^a Faculty of Engineering and Computing   (United Kingdom)

^b CURTIN UNIVERSITY   (Australia)

Author keywords

Equilibrium points; Positive systems; Stability

Indexed keywords

CONFERENCE PAPER; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; POSITIVE LINEAR DISCRETE TIME SYSTEM; TIME;

EID: 18544383738     PISSN: 02397285     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Conference Paper

References (22)

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. th 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. th 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 non-negative 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).