Minimum energy control of fractional positive continuous-time linear systems with bounded inputs
References
- 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 Sciences56(4): 319–324.
- Dzieliński, A., Sierociuk, D. and Sarwas, G. (2009). Ultracapacitor parameters identification based on fractional order model, Proceedings of ECC’09, Budapest, Hungary.
- Dzieliński, A. and Sierociuk, D. (2008). Stability of discrete fractional order state-space systems, Journal of Vibrations and Control14(9/10): 1543–1556.
- Farina, L. and Rinaldi, S. (2000). Positive Linear Systems: Theory and Applications, J. Wiley, New York, NY.
- Kaczorek, T. (1992). Linear Control Systems, Research Studies Press and J. Wiley, New York, NY.
- Kaczorek, T. (2001). Positive 1D and 2D Systems, Springer-Verlag, London.
- Kaczorek, T. (2008a). Fractional positive continuous-time systems and their reachability, International Journal of Applied Mathematics and Computer Science18(2): 223–228, DOI: 10.2478/v10006-008-0020-0.
- Kaczorek, T. (2008b). Practical stability of positive fractional discrete-time linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences56(4): 313–317.
- Kaczorek, T. (2008c). Reachability and controllability to zero tests for standard and positive fractional discrete-time systems, Journal Européen des Systémes Automatisés42(6–8): 769–787.
- Kaczorek, T. (2009). Asymptotic stability of positive fractional 2D linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences57(3): 289–292.
- Kaczorek, T. (2011a). Controllability and observability of linear electrical circuits, Electrical Review87(9a): 248–254.
- Kaczorek, T. (2011b). Positivity and reachability of fractional electrical circuits, Acta Mechanica et Automatica5(2): 42–51.
- Kaczorek, T. (2011c). Positive linear systems consisting of n subsystems with different fractional orders, IEEE Transactions Circuits and Systems58(6): 1203–1210.
- Kaczorek, T. (2011d). Checking of the positivity of descriptor linear systems by the use of the shuffle algorithm, Archive of Control Sciences21(3): 287–298.
- Kaczorek, T. (2012). Selected Problems of Fractional Systems Theory, Springer-Verlag, Berlin.
- Kaczorek, T. (2013a). Minimum energy control of fractional positive continuous-time linear systems, MMAR 2013, Międzyzdroje, Poland.
- Kaczorek, T. (2013c). Minimum energy control of positive discrete-time linear systems with bounded inputs, Archives of Control Sciences23(2): 205–211.
- Kaczorek, T. (2013d). Minimum energy control of positive continuous-time linear systems with bounded inputs, International Journal of Applied Mathematics and Computer Science23(4): 725–730, DOI: 10.2478/amcs-2013-0054.
- Kaczorek, T. (2014a). Minimum energy control of descriptor positive discrete-time linear systems, COMPEL33(3)
- 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 Sciences62(2), (in press).
- Kaczorek, T. and Klamka, J. (1986). Minimum energy control of 2D linear systems with variable coefficients, International Journal of Control44(3): 645–650.
- Klamka, J. (1976a). Relative controllability and minimum energy control of linear systems with distributed delays in control, IEEE Transactions on Automatic Control21(4): 594–595.
- Klamka, J. (1976b). Relative controllability and minimum energy control of linear systems with distributed delays in control, IEEE Transactions on Automatic Control21(4): 594–595.
- Klamka, J. (1977). Minimum energy control of discrete systems with delays in control, International Journal of Control26(5): 737–744.
- Klamka, J. (1983). Minimum energy control of 2D systems in Hilbert spaces, System Sciences9(1–2): 33–42.
- Klamka, J. (1991). Controllability of Dynamical Systems, Kluwer Academic Press, Dordrecht.
- 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.
- Oldham, K.B. and Spanier, J. (1974). The Fractional Calculus, Academic Press, New York, NY.
- Ostalczyk, P. (2008). Epitome of the Fractional Calculus: Theory and Its Applications in Automatics, Technical University of Łódź Press, Łódź, (in Polish).
- Podlubny, I. (1999). Fractional Differential Equations, Academic Press, San Diego, CA.
- 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 Fractals40(5): 2317–2328.
- 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.
- Vinagre, B.M. (2002). Fractional order systems and fractional order control actions, IEEE CDC’02, Las Vegas, USA, NV, TW#2, Lecture 3.
Language: English
Page range: 335 - 340
Submitted on: Aug 24, 2013
Published on: Jun 26, 2014
Published by: University of Zielona Góra
In partnership with: Paradigm Publishing Services
Publication frequency: 4 times per year
Related subjects:
© 2014 Tadeusz Kaczorek, published by University of Zielona Góra
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.