Controllability criteria for time–delay fractional systems with a retarded state
By:
References
- Babiarz, A., Grzejszczak, T., Łegowski, A. and Niezabitowski, M. (2016). Controllability of discrete-time switched fractional order systems, Proceedings of the 12th World Congress on Intelligent Control and Automation, Guilin, China, pp. 1754–1757.
- Balachandran, K. and Kokila, J. (2012). On the controllability of fractional dynamical systems, International Journal and Applied Mathematics and Computer Science22(3): 523–531, DOI: 10.2478/v10006-012-0039-0.
- Balachandran, K. and Kokila, J. (2013). Controllability of fractional dynamical systems with prescribed controls, IET Control Theory and Applications7(9): 1242–1248.
- Balachandran, K., Kokila, J. and Trujillo, J. (2012a). Relative controllability of fractional dynamical systems with multiple delays in control, Computers and Mathematics with Appllications64(10): 3037–3045.
- Balachandran, K., Park, J. and Trujillo, J. (2012b). Controllability of nonlinear fractional dynamical systems, Nonlinear Analysis75(4): 1919–1926.
- Balachandran, K., Zhou, Y. and Kokila, J. (2012c). Relative controllability of fractional dynamical systems with delays in control, Communications in Nonlinear Science and Numerical Simulation17(9): 3508–3520.
- Busłowicz, M. (2012). Stability analysis of continuous-time linear systems consisting of n subsystems with different fractional orders, Bulletin of the Polish Academy of Sciences: Technical Sciences60(2): 270–284.
- Busłowicz, M. (2014). Controllability, reachability and minimum energy control of fractional discrete-time linear systems with multiple delays in state, Bulletin of the Polish Academy of Sciences: Technical Sciences62(2): 233–239.
- Chen, Y., Ahn, H. and Xue, D. (2006). Robust controllability of interval fractional order linear time invariant systems, Signal Processes86(10): 2794–2802.
- Chikriy, A. and Matichin, I. (2008). Presentation of solutions of linear systems with fractional derivatives in the sense of Riemann–Liouville, Caputo and Miller–Ross, Journal of Automation and Information Science40(6): 1–11.
- Chukwu, E. (1979). Euclidean controllability of linear delay systems with limited controls, IEEE Transactions on Automatic Control24(5): 798–800.
- Deng, W., Li, C. and Lu, J. (2007). Stability analysis of linear fractional differential systems with multiple time delays, Nonlinear Dynamics48: 409–416.
- Kaczorek, T. (2011). Selected Problems of Fractional Systems Theory, Lecture Notes in Control and Information Science, Vol. 411, Springer-Verlag, Berlin/Heidelberg.
- Kaczorek, T. (2014a). 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): 227–231.
- Kaczorek, T. (2014b). Minimum energy control of fractional positive continuous-time linear systems with bounded inputs, International Journal of Applied Mathematics and Computer Science24(2): 335–340, DOI: 10.2478/amcs-2014-0025.
- Kaczorek, T. and Rogowski, K. (2015). Fractional Linear Systems and Electrical Circuits, Studies in Systems, Decision and Control, Vol. 13, Springer International Publishing, Cham.
- Kilbas, A., Srivastava, H. and Trujillo, J. (2006). Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, Vol. 204, Elsevier, Amsterdam.
- Klamka, J. (1991). Controllability of Dynamical Systems, Kluwer Academic Publishers, Dordrecht.
- Klamka, J. (2008). Constrained controllability of semilinear systems with delayed controls, Bulletin of the Polish Academy of Sciences: Technical Sciences56(4): 333–337.
- Klamka, J. (2009). Constrained controllability of semilinear systems with delays, Nonlinear Dynamics56(1): 169–177.
- Klamka, J. (2010). Controllability and minimum energy control problem of fractional discrete-time systems, in D. Balenau (Ed.), New Trends Nanotechology and Fractional Calculus Applications, Springer, Dordrecht, pp. 503–509.
- Klamka, J. (2011). Local controllability of fractional discrete-time semilinear systems, Acta Mechanica at Automatica5(2): 55–58.
- Klamka, J., Czornik, A., Niezabitowski, M. and Babiarz, A. (2014). Controllability and minimum energy control of linear fractional discrete-time infinite-dimensional Controllability criteria for time-delay fractional systems with a retarded state systems, Proceedings of the 11th IEEE International Conference on Control and Automation, Taichung, Taiwan, pp. 1210–1214.
- Lee, E. and Marcus, L. (1967). Foundations of Optimal Control Theory, John Wiley and Sons, New York, NY.
- Manitius, A. (1974). Optimal control of hereditary systems, in J.W. Weil (Ed.), Control Theory and Topics in Functional Analysis, Vol. 3, International Centre for Theoretical Physics, Trieste, pp. 43–178.
- Miller, K. and Ross, B. (1993). An Introduction to the Fractional Calculus and Fractional Differential Calculus, John Wiley andSons, New York, NY.
- Monje, A., Chen, Y., Viagre, B., Xue, D. and Feliu, V. (2010). Fractional-Order Systems and Control: Fundamentals and Applications, Springer-Verlag, London.
- Oldham, K. and Spanier, J. (1974). The Fractional Calculus, Academic Press, New York, NY.
- Pawłuszewicz, E. and Mozyrska, D. (2013). Constrained controllability of h-difference linear systems with two fractional orders, in W. Mitkowski et al. (Ed.), Advances in the Theory and Applications of Non-integer Order Systems, Lecture Notes in Electrical Engineering, Vol. 257, Springer International Publishing, Cham, pp. 67–75.
- Podlubny, I. (1999). Fractional Differential Equations, Academic Press, San Diego, CA.
- Rolewicz, S. (1987). Functional Analysis and Control Theory: Linear Systems, Mathematics and Its Applications, Springer, Dordrecht.
- Sabatier, J., Agrawal, O. and Tenreiro Machado, J. (Eds.) (2007). Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, Springer-Verlag, Dordrecht.
- Sakthivel, R., Ren, Y. and Mahmudov, N. (2011). On the approximate controllability of semilinear fractional differential systems, Computers and Mathematics with Applications62(3): 1451–1459.
- Samko, S., Kilbas, A. and Marichev, O. (1993). Fractional Integrals and Derivatives: Theory and Applications, Gordan and Breach Science Publishers, Philadelphia, PA.
- Sikora, B. (2003). On the constrained controllability of dynamical systems with multiple delays in the state, International Journal of Applied Mathematics and Computer Science13(4): 469–479.
- Sikora, B. (2005). On constrained controllability of dynamical systems with multiple delays in control, Applicationes Mathematicae32(1): 87–101.
- Sikora, B. (2016). Controllability of time-delay fractional systems with and without constraints, IET Control Theory and Applications10(3): 320–327.
- Sikora, B. and Klamka, J. (2012). On constrained stochastic controllability of dynamical systems with multiple delays in control, Bulletin of the Polish Academy of Sciences: Technical Sciences60(12): 301–305.
- Trzasko, B. (2008). Reachability and controllability of positive fractional discrete-time systems with delay, Journal of Automation Mobile Robotics and Intelligent Systems2(3): 43–47.
- Wang, J. and Zhou, Y. (2012). Complete controllability of fractional evolution systems, Communications in Nonlinear Science and Numerical Simulation17(11): 4346–4355.
- Wei, J. (2012). The controllability of fractional control systems with control delay, Computers and Mathematics with Applications64(10): 3153–3159.
- Zhang, H., Cao, J. and Jiang, W. (2013). Controllability criteria for linear fractional differential systems with state delay and impulses, Journal of Applied Mathematics, Article ID: 146010.
- Zhao, X., Liu, X., Yin, S. and Li, H. (2013). Stability of a class of switched positive linear time-delay systems, International Journal of Robust and Nonlinear Control23(5): 578–589.
- Zhao, X., Liu, X., Yin, S. and Li, H. (2014). Improved results on stability of continuous-time switched positive linear systems, Automatica50(2): 614–621.
Language: English
Page range: 521 - 531
Submitted on: Dec 16, 2015
Accepted on: May 10, 2016
Published on: Sep 29, 2016
Published by: University of Zielona Góra
In partnership with: Paradigm Publishing Services
Publication frequency: 4 times per year
Keywords:
Related subjects:
© 2016 Beata Sikora, published by University of Zielona Góra
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.