On the asymptotic stability of positive 2-D systems described by the Roesser model

IEEE Transactions on Circuits and Systems II: Express Briefs

Volumn 54, Issue 12, 2007, Pages 1102-1104

  Chu, Bing ^a   Liu, Yanhong ^b  

^a UNIVERSITY OF SHEFFIELD   (United Kingdom)

^b ZHENGZHOU UNIVERSITY   (China)

Author keywords

2 D systems; Asymptotic stability; Positive systems; Roesser model

Indexed keywords

ASYMPTOTIC STABILITY;

1D SYSTEMS; 2-D SYSTEMS; ANALYSIS AND SYNTHESIS; POSITIVE SYSTEMS; ROESSER MODELS; SYSTEM MATRICES;

SYSTEM STABILITY;

EID: 57149145931     PISSN: 15497747     EISSN: 15583791     Source Type: Journal    
DOI: 10.1109/TCSII.2007.908899     Document Type: Article

References (23)

1. A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences. New York: Academic, 1979.
2. R. A. Brualdi and H. J. Ryser, Combinatorial Matrix Theory. Cambridge, U.K.: Cambridge Univ. Press, 1991.
3. H. Maeda and S. Kodama, "Positive realization of difference equations," IEEE Trans. Circuits Syst., vol. CAS-28, pp. 39-47, Jan. 1981.
4. H. Minc, Nonnegative Matrices. New York: Wiley, 1988.
5. L. Benvenuti, A. D. Santis, and L. Farina, Eds., in Proc. 1st Multidisciplinary Int. Symp. Positive Systems, Rome, Italy, Aug. 28-30, 2003.
6. N. K. Bose, Applied Multidimensional System Theory. New York: Van Nostrand Reinhold, 1982.
7. T. Kaczorek, Two-Dimensional Linear Systems. Berlin, Germany: Springer-Verlag, 1985.
8. K. Galkowski, "Multi-dimensional systems theory - A common approach to problems in circuits, control and signal processing," in Proc. IEE Colloquium on Multi-Dimensional Systems: Problems and Solutions, Jan. 1996.
9. T. Kaczorek, Positive 1-D and 2-D Systems. New York: Springer, c2002.
10. E. Fornasini, "A 2-D systems approach to river pollution modeling," Multidim.Syst. Signal Processing, vol. 2, pp. 233-265, Aug. 1991.
11. W. P. Heath, Self-Tuning Control for Two-Dimensional Processes. New York: Wiley, 1994.
12. S. Vomiero, "Un'Applicazione dei Sistemi 2-D alla Modellistica dello ScambioSangue-Tessuto," Master's thesis, Dip. Elettronica ed Informatica, Univ. di Padova (I), Padova, Italy, 1992.
13. T. Kaczorek, "Reachability and controllability of nonnegative 2-D Roesser type models," Bull. Pol. Acad. Sci., Ser. Tech. Sci., vol. 44, no. 4, pp. 405-410, 1996.
14. T. Kaczorek, "Realization problem, reachability and minimum energy control of positive 2-D Roesser model," in Proc. 6th Ann. Int. Conf. Advances in Communication and Control, 1997, pp. 765-776.
15. T. Kaczorek, L. Benvenuti, A. D. Santis, and L. Farina, Eds., "Some recent developments in positive 2-D systems," in Proc. 1st Multidisciplinary Int. Symp. Positive Systems, Rome, Italy, 2003, pp. 329-337.
16. E. Bailo, R. Bru, J. Gelonch, and S. Romero, "On the reachability index of positive 2-D systems," IIEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 53, no. 10, pp. 997-1001, Oct. 2006.
17. E. Fornasini and M. E. Valcher, "Controllability and reachability of 2-D positive systems: A graph theoretic approach," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 52, no. 3, pp. 576-585, Mar. 2005.
18. J. E. Kurek, "Stability of positive 2-D system described by the Roesser model," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 49, no. 4, pp. 531-533, Apr. 2002.
19. D. D. Givone and R. P. Roesser, "Multidimensional linear iterative circuits-general properties," IEEE Trans. Comput., vol. COM-21, no. 10, pp. 1067-1073, Oct. 1972.
20. P. Lancaster, The Theory of Matrices with Applications. Orlando, FL: Academic, 1985.
21. A. Packard and J. C. Doyle, "The complex structured singular value," Automatica, vol. 29, pp. 71-109, Jan. 1993.
22. K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control. Upper Saddle River, NJ: Prentice-Hall, 1996.
23. R. P. Braatz, P. M. Young, J. C. Doyle, and M. Morari, "Computational complexity of μ calculation," IEEE Trans. Autom. Contr., vol. 39, no. 5, pp. 1000-1002, May 1994.