Minimum energy control of fractional positive continuous-time linear systems with bounded inputs

 Access to full text

 Full (PDF)

 Access to full text

1. Busłowicz, M. (2008). Stability of linear continuous time fractional order systems with delays of the retarded type, Bulletin of the Polish Academy of Sciences: Technical Sciences 56(4): 319-324. 
2. Dzieliński, A., Sierociuk, D. and Sarwas, G. (2009). Ultracapacitor parameters identification based on fractional order model, Proceedings of ECC'09, Budapest, Hungary. Zbl1268.34091
3. Dzieliński, A. and Sierociuk, D. (2008). Stability of discrete fractional order state-space systems, Journal of Vibrations and Control 14(9/10): 1543-1556. Zbl1229.93143
4. Farina, L. and Rinaldi, S. (2000). Positive Linear Systems: Theory and Applications, J. Wiley, New York, NY. Zbl0988.93002
5. Kaczorek, T. (1992). Linear Control Systems, Research Studies Press and J. Wiley, New York, NY. Zbl0784.93002
6. Kaczorek, T. (2001). Positive 1D and 2D Systems, Springer-Verlag, London. Zbl1005.68175
7. Kaczorek, T. (2008a). Fractional positive continuous-time systems and their reachability, International Journal of Applied Mathematics and Computer Science 18(2): 223-228, DOI: 10.2478/v10006-008-0020-0. Zbl1235.34019
8. Kaczorek, T. (2008b). Practical stability of positive fractional discrete-time linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 56(4): 313-317. 
9. Kaczorek, T. (2008c). Reachability and controllability to zero tests for standard and positive fractional discrete-time systems, Journal Européen des Systémes Automatisés 42(6-8): 769-787. 
10. Kaczorek, T. (2009). Asymptotic stability of positive fractional 2D linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 57(3): 289-292. 
11. Kaczorek, T. (2011a). Controllability and observability of linear electrical circuits, Electrical Review 87(9a): 248-254. 
12. Kaczorek, T. (2011b). Positivity and reachability of fractional electrical circuits, Acta Mechanica et Automatica 5(2): 42-51. 
13. Kaczorek, T. (2011c). Positive linear systems consisting of n subsystems with different fractional orders, IEEE Transactions Circuits and Systems 58(6): 1203-1210. 
14. Kaczorek, T. (2011d). Checking of the positivity of descriptor linear systems by the use of the shuffle algorithm, Archive of Control Sciences 21(3): 287-298. Zbl1264.93096
15. Kaczorek, T. (2012). Selected Problems of Fractional Systems Theory, Springer-Verlag, Berlin. Zbl1221.93002
16. Kaczorek, T. (2013a). Minimum energy control of fractional positive continuous-time linear systems, MMAR 2013, Międzyzdroje, Poland. Zbl1285.49002
17. Kaczorek, T. (2013c). Minimum energy control of positive discrete-time linear systems with bounded inputs, Archives of Control Sciences 23(2): 205-211. Zbl1291.93183
18. Kaczorek, T. (2013d). Minimum energy control of positive continuous-time linear systems with bounded inputs, International Journal of Applied Mathematics and Computer Science 23(4): 725-730, DOI: 10.2478/amcs-2013-0054. Zbl1285.49002
19. Kaczorek, T. (2014a). Minimum energy control of descriptor positive discrete-time linear systems, COMPEL 33(3) Zbl1309.93093
20. Kaczorek, T. (2014b). An extension of Klamka's method of minimum energy control to fractional positive discrete-time linear systems with bounded inputs, Bulletin of the Polish Academy of Sciences: Technical Sciences 62(2), (in press). 
21. Kaczorek, T. and Klamka, J. (1986). Minimum energy control of 2D linear systems with variable coefficients, International Journal of Control 44(3): 645-650. Zbl0637.93044
22. Klamka, J. (1976a). Relative controllability and minimum energy control of linear systems with distributed delays in control, IEEE Transactions on Automatic Control 21(4): 594-595. Zbl0332.93013
23. Klamka, J. (1976b). Relative controllability and minimum energy control of linear systems with distributed delays in control, IEEE Transactions on Automatic Control 21(4): 594-595. Zbl0332.93013
24. Klamka, J. (1977). Minimum energy control of discrete systems with delays in control, International Journal of Control 26(5): 737-744. Zbl0412.49022
25. Klamka, J. (1983). Minimum energy control of 2D systems in Hilbert spaces, System Sciences 9(1-2): 33-42. Zbl0574.93009
26. Klamka, J. (1991). Controllability of Dynamical Systems, Kluwer Academic Press, Dordrecht. Zbl0732.93008
27. Klamka, J. (2010). Controllability and minimum energy control problem of fractional discrete-time systems, in D. Baleanu, Z.B. Guvenc and J.A. Tenreiro Machado (Eds.), New Trends Nanotechology and Fractional Calculus, Springer-Verlag, New York, NY, pp. 503-509. Zbl1222.93030
28. Oldham, K.B. and Spanier, J. (1974). The Fractional Calculus, Academic Press, New York, NY. Zbl0292.26011
29. Ostalczyk, P. (2008). Epitome of the Fractional Calculus: Theory and Its Applications in Automatics, Technical University of Łódź Press, Łódź, (in Polish). 
30. Podlubny, I. (1999). Fractional Differential Equations, Academic Press, San Diego, CA. Zbl0924.34008
31. Radwan, A.G., Soliman, A.M., Elwakil, A.S. and Sedeek, A. (2009). On the stability of linear systems with fractional-order elements, Chaos, Solitons and Fractals 40(5): 2317-2328. Zbl1198.93151
32. Solteiro Pires, E.J., Tenreiro Machado, J.A. and Moura Oliveira, P.B. (2006). Fractional dynamics in genetic algorithms, Workshop on Fractional Differentiation and Its Application, Porto, Portugal, Vol. 2, pp. 414-419. 
33. Vinagre, B.M. (2002). Fractional order systems and fractional order control actions, IEEE CDC'02, Las Vegas, USA, NV, TW#2, Lecture 3. 

1. Tadeusz Kaczorek, Positivity and linearization of a class of nonlinear continuous-time systems by state feedbacks
2. Beata Sikora, Controllability criteria for time-delay fractional systems with a retarded state