Minimum Energy Control of Fractional Discrete-Time Linear Systems with Delays in State and Control

1. Buslowicz, M.: On some properties of the solution of state equation of discrete-time systems with delays. Zesz. Nauk. Polit. Bial., Elektrotechnika (1), 17–29 (1983) (in Polish)

   Google Scholar 

2. Busłowicz, M., Kaczorek, T.: Reachability and minimum energy control of positive linear discrete-time systems with multiple delays in state and control. Measurement Automation and Monitoring 53(10), 40–45 (2007)

   Google Scholar 

3. Busłowicz M.: Controllability, reachability and minimum energy control of fractional discrete-time linear systems with multiple delays in state. Bull. Pol. Acad.: Tech. (in print)

   Google Scholar 

4. Dzieliński, A., Sierociuk, D., Sarwas, G.: Some applications of fractional order calculus. Bull. Pol. Acad. Scie.: Tech. 58(4), 583–592 (2010)

   MATH  Google Scholar 

5. Guermach, S., Djennoune, S., Bettayeb, M.: Controllability and observability of linear discrete-time fractional-order systems. Int. J. Appl. Math. Comput. Sci. 18(2), 213–222 (2008)

   MathSciNet  Google Scholar 

6. Kaczorek, T., Klamka, J.: Minimum energy control of 2D linear systems with variable coefficients. Int. J. of Control 44(3), 645–650 (1986)

   Article  MATH  MathSciNet  Google Scholar 

7. Kaczorek, T.: Vectors and matrices in automatics and electrotechnics. WNT, Warsaw (1998)

   Google Scholar 

8. Kaczorek, T.: Selected Problems of Fractional Systems Theory. LNCIS, vol. 411. Springer, Heidelberg (2011)

   MATH  Google Scholar 

9. Kaczorek, T.: Minimum energy control of fractional positive continuous-time linear systems. In: Proc. 18th Int. Conference Methods and Models in Automation and Robotics, Międzyzdroje, Poland, pp. 622–626 (2013) (CD-ROM)

   Google Scholar 

10. Kaczorek, T.: Minimum energy control of fractional positive continuous-time linear systems with bounded inputs. Int. J. Appl. Math. Comput. Sci. (in print)

    Google Scholar 

11. Kaczorek, T.: An extension of Klamka’s method of minimum energy control to fractional positive discrete-time linear systems with bounded inputs. Bull. Pol. Acad.: Tech. 62(1) (2014) (in print)

    Google Scholar 

12. Klamka, J.: Relative controllability and minimum energy control of linear systems with distributed delays in control. IEEE Trans. on Automatic Control AC-21(4), 594–595 (1976)

    Article  MathSciNet  Google Scholar 

13. Klamka, J.: Minimum energy control of discrete systems with delays in control. Int. J. Control 26(5), 737–744 (1977)

    MATH  MathSciNet  Google Scholar 

14. Klamka, J.: Minimum energy control of 2D systems in Hilbert spaces. Systems Science 9(1-2), 33–42 (1983)

    MathSciNet  Google Scholar 

15. Klamka, J.: Controllability of Dynamical Systems. Kluwer Acad. Publ., Dordrecht (1991)

    MATH  Google Scholar 

16. Klamka, J.: Controllability and minimum energy control problem of infinite dimensional fractional discrete-time systems with delays. In: Proc. First Asian Conference on Intelligent Information and Database Systems, Dong Hoi City, Vietnam, pp. 398–403 (2009)

    Google Scholar 

17. Klamka, J.: Controllability and minimum energy control problem of fractional discrete-time systems. In: Baleanu, D. (ed.) New Trends in Nanotechnology and Fractional Calculus Applications, pp. 503–509. Springer, New York (2010)

    Chapter  Google Scholar 

18. Kociszewski, R.: Controllability and observability of linear time-invariant positive discrete-time systems with delays. PhD Dissertation, Faculty of Electrical Engineering, Bialystok University of Technology, Bialystok (2008) (in Polish)

    Google Scholar 

19. Luo, Y., Chen, Y.-Q.: Fractional Order Motion Controls. John Wiley & Sons Ltd, Chichester (2013)

    Google Scholar 

20. Monje, C.A., Chen, Y.Q., Vinagre, B.M., Xue, D., Feliu-Batlle, V.: Fractional-order Systems and Controls Fundamentals and Applications. Springer, London (2010)

    Book  MATH  Google Scholar 

21. Mozyrska, D., Pawłuszewicz, E.: Local controllability of nonlinear discrete-time fractional order systems. Bull. Pol. Ac.: Tech. 61(1), 251–256 (2013)

    Google Scholar 

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

    MATH  Google Scholar 

23. Trzasko, W.: Reachability and controllability of positive fractional discrete-time systems with delay. Journal of Automation, Mobile Robotics & Intelligent Systems 2(3), 43–47 (2008)

    Google Scholar 

Download references