A new approach to the internally positive representation of linear mimo systems

IEEE Transactions on Automatic Control

Volumn 57, Issue 1, 2012, Pages 119-134

  Cacace, Filippo ^a   Germani, Alfredo ^b   Manes, Costanzo ^b   Setola, Roberto ^a  

^a UNIVERSITY CAMPUS BIO MEDICO   (Italy)

^b UNIVERSITY OF L'AQUILA   (Italy)

Author keywords

Internally positive representation; Linear systems; Positive systems; State space realization

Indexed keywords

COMPLEX VECTORS; COMPUTATIONAL COSTS; CONTROL LAWS; FIBER-OPTIC FILTER; FINITE DIMENSIONS; INTERNALLY POSITIVE REPRESENTATION; POSITIVE SYSTEMS; REDUCED ORDER; ROUTING NETWORKS; STABILITY PROPERTIES; STABLE SYSTEMS; STATE OBSERVER; STATE SPACE REALIZATION; STATE-SPACE;

FIBER OPTIC NETWORKS; LINEAR SYSTEMS; MIMO SYSTEMS; SIGNAL PROCESSING; STABILITY;

OBSERVABILITY;

EID: 84855384215     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2011.2158170     Document Type: Article

References (24)

1. B. D. O. Anderson, M. Deistler, L. Farina, and L. Benvenuti, "Nonnegative realization of a linear system with nonnegative impulse response," IEEE Trans. Circuits Syst. I, vol. 43, no. 2, pp. 134-142, 1996. (Pubitemid 126776650)
2. R. M. Anderson and R. M. May, "Population biology of infectious diseases: Part I," Nature, vol. 280, pp. 361-367, 1979.
3. A. Asachenkov, G. Marchuk, R. Mohler, and S. Zuev, Disease Dynamics. Boston, MA: Birkhauser, 1994.
4. L. Benvenuti and L. Farina, "On the class of linear filters attainable with charge routing networks," IEEE Trans. Circ. Syst.-II, vol. 43, pp. 618-622, 1996. (Pubitemid 126777607)
5. L. Benvenuti and L. Farina, "Discrete-time filtering via charge routing networks," Signal Process., vol. 49, pp. 207-215, 1996. (Pubitemid 126349427)
6. L. Benvenuti, L. Farina, and B. D. O. Anderson, "Filtering through combination of positive filters," IEEE Trans. Circ. Syst.-I: Fundamental Theory and Applications, vol. 46, no. 12, pp. 1431-1440, 1999. (Pubitemid 30558660)
7. L. Benvenuti and L. Farina, "The design of fiber-optic filters," J. Lightw. Technol., vol. 19, no. 9, pp. 1366-1375, 2001. (Pubitemid 32949874)
8. L. Benvenuti and L. Farina, "A tutorial on the positive realization problem," IEEE Trans. Autom. Control, vol. 49, no. 5, pp. 651-664, 2004.
9. F. Cacace, A. Germani, and C. Manes, "Representation of a class of polynomial MIMO systems via positive realizations," in Proc. Eur. Control Conf. (ECC09), Budapest, Hungary, Aug. 2009.
10. W. Czaja, P. Jaming, and M. Matolsci, "An efficient algorithm for positive realizations," Syst. Control Lett., vol. 57, no. 5, pp. 436-441, 2008. (Pubitemid 351417666)
11. A. Germani, C. Manes, and P. Palumbo, "State representation of a class of MIMO systems via positive systems," in Proc. IEEE Conf. Decision and Control, New Orleans, LA, Dec. 2007.
12. A. Germani, C. Manes, and P. Palumbo, "Representation of a class of MIMO systems via internally positive realization," Eur. J. Control, vol. 16, no. 3, pp. 291-304, 2010.
13. A. Gersho and B. Gopinath, "Charge-routing networks," IEEE Trans. Circ. and Syst, vol. 26, no. 2, pp. 81-92, 1979.
14. F. I. Karpelevich, "On the characteristic roots of matrices with nonnegative elements," in Eleven Papers Translated From Russian. Providence, RI: American Math. Soc., 1988, vol. 140.
15. Y. Y. Haimes, B. M. Horowitz, J. H. Lambert, J. R. Satos, L. Chenyang, and K. G. Crowther, "Inoperability input-output model for interdependent infrastructure sectors. I: Theory and methodology," J. Infrastruct. Syst., vol. 11, no. 2, pp. 67-79, 2005. (Pubitemid 40864758)
16. W. W. Leontieff, The Structure of the American Economy 1919-1939. New York: Oxford Univ. Press, 1951.
17. P. H. Leslie, "On the use of matrices in certain population mathematics," Biometrika, vol. 33, pp. 183-212
18. D. G. Luenberger, Introduction to Dynamic Systems. Hoboken, NJ: Wiley, 1979.
19. B. Nagy and M. Matolcsi, "Minimal positive realizations of transfer functions with nonnegative multiple poles," IEEE Trans. Autom. Contr., vol. 50, pp. 1447-1450, 2005. (Pubitemid 41388190)
20. B. Nagy,M.Matolcsi, and M. Szilvási, "Order bound for realization of a combination of positive filters," IEEE Trans. Autom. Contr., vol. 52, pp. 724-729, 2007. (Pubitemid 46621599)
21. C. D. Mayer, Matrix Analysis and Applied Linear Algebra. Philadelphia, PA: SIAM, 2000.
22. S. Rinaldi and L. Farina, Positive Linear Systems: Theory and Applications. Hoboken, NJ : Wiley, 2000.
23. V.Volterra, "Variations and fluctuations of the number of individuals in animal species living together," in Animal Ecology. New York: Mc-Graw-Hill
24. L. Yuzhe and P. H. Bauer, "Frequency domain limitations in the design of nonnegative impulse response filters," IEEE Trans. Signal Process., vol. 58, no. 9, pp. 4535-4546, Sep. 2010.