Digraphs Minimal Realisations of State Matrices for Fractional Positive Systems

1. Benvenuti, L., Farina, L.: Positive and compartmental systems. IEEE Transactions on Automatic Control (47), 370–373 (2002)

   Google Scholar 

2. Benvenuti, L., Farina, L.: A tutorial on the positive realization problem. IEEE Transactions on Automatic Control 49(5), 651–664 (2004)

   Article  MathSciNet  Google Scholar 

3. Berman, A., Neumann, M., Stern, R.J.: Nonnegative Matrices in Dynamic Systems. Wiley, New York (1989)

   MATH  Google Scholar 

4. Farina, L., Rinaldi, S.: Positive linear systems: theory and applications. Wiley-Interscience, Series on Pure and Applied Mathematics, New York (2000)

   Book  Google Scholar 

5. Fornasini, E., Valcher, M.E.: Directed graphs, 2D state models, and characteristic polynomials of irreducible matrix pairs. Linear Algebra and Its Applications 263, 275–310 (1997)

   Article  MATH  MathSciNet  Google Scholar 

6. Fornasini, E., Valcher, M.E.: On the positive reachability of 2D positive systems. In: Benvenuti, L., De Santis, A., Farina, L. (eds.) Positive Systems. LNCIS, vol. 294, pp. 297–304. Springer, Heidelberg (2003)

   Chapter  Google Scholar 

7. Horn, R.A., Johnson, C.R.: Topics in Matrix Analysis. Cambridge Univ. Press (1991)

   Google Scholar 

8. Hryniów, K., Markowski, K.A.: Parallel digraphs-building algorithm for polynomial realisations. In: Proceedings of 2014 15th International Carpathian Control Conference (ICCC), pp. 174–179 (2014), http://dx.doi.org/10.1109/CarpathianCC.2014.6843592

9. Hryniów, K., Markowski, K.A.: Reachability index calculation by parallel digraphs-building. In: 19th International Conference on Methods and Models in Automation and Robotics (MMAR), Miedzyzdroje, Poland, September 2-5, pp. 808–813 (2014), http://dx.doi.org/10.1109/MMAR.2014.6957460

10. Hryniów, K., Markowski, K.A.: Digraphs-building of complete set of minimal characteristic polynomial realisations as means for solving minimal realisation problem of nD systems. International Journal of Control (Submitted to)

    Google Scholar 

11. Kaczorek, T.: Two-dimensional Linear Systems. Springer, London (1985)

    MATH  Google Scholar 

12. Kaczorek, T.: Positive 1D and 2D systems. Springer, London (2001)

    Google Scholar 

13. Kaczorek, T.: Positive realization for 2D systems with delays. In: Proceedings of 2007 International Workshop on Multidimensional (nD) Systems, pp. 137–141. IEEE (2007)

    Google Scholar 

14. Kaczorek, T.: Realization problem for positive 2D hybrid systems. COMPEL 27(3), 613–623 (2008)

    Article  MATH  MathSciNet  Google Scholar 

15. Kaczorek, T.: Selected Problems of Fractional Systems Theory. Springer, Berlin (2011)

    Book  MATH  Google Scholar 

16. Luenberger, D.G.: Positive linear systems. In: Introduction to Dynamic Systems: Theory, Models, and Applications. Wiley, New York (1979)

    Google Scholar 

17. Miller, K., Ross, B.: An Introduction to the Fractional Calculus and Fractional Differenctial Equations. Willeys, New York (1993)

    Google Scholar 

18. Nishimoto, K.: Fractional Calculus. Decartess Press, Koriama (1984)

    MATH  Google Scholar 

19. Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)

    MATH  Google Scholar 

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