Abstract
In the article unconstrained controllability problem of positive discrete-time switched fractional order systems is addressed. A solution of discrete-time switched fractional order systems is presented. Additionally, a transition matrix of considered dynamical systems is given. A sufficient condition for unconstrained controllability in a given number of steps is formulated and proved using the general formula of solution of difference state equation. Finally, the illustrative examples are also presented.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Babiarz, A., Czornik, A., Klamka, J., Niezabitowski, M.: The selected problems of controllability of discrete-time switched linear systems with constrained switching rule. Bull. Polish Acad. Sci. Tech. Sci. 63(3), 657–666 (2015)
Babiarz, A., Klamka, J.: Controllability of discrete linear time-varying fractional system with constant delay. In: 13th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM). AIP Conference Proceedings, Rhodes, Greece, 23–29 September, pp. 480058(1)–480058(4) (2015)
Babiarz, A., Czornik, A., Niezabitowski, M.: Output controllability of the discrete-time linear switched systems. Nonlinear Anal. Hybrid Syst. 21, 1–10 (2016)
Badri, V., Tavazoei, M.S.: On tuning fractional order [proportional-derivative] controllers for a class of fractional order systems. Automatica 49(7), 2297–2301 (2013)
Bashirov, A.E., Kerimov, K.R.: On controllability conception for stochastic systems. SIAM J. Control Optim. 35(2), 384–398 (1997)
Bashirov, A.E., Mahmudov, N.I.: On concepts of controllability for deterministic and stochastic systems. SIAM J. Control Optim. 37(6), 1808–1821 (1999)
Benchohra, M., Ouahab, A.: Controllability results for functional semilinear differential inclusions in Fréchet spaces. Nonlinear Anal. Theor. Methods Appl. 61(3), 405–423 (2005)
Czornik, A., Świerniak, A.: On controllability with respect to the expectation of discrete time jump linear systems. J. Franklin Inst. 338(4), 443–453 (2001)
Czornik, A., Świerniak, A.: On direct controllability of discrete time jump linear system. J. Franklin Inst. 341(6), 491–503 (2004)
Kaczorek, T.: Selected Problems of Fractional Systems Theory, vol. 411. Springer Science & Business Media, Heidelberg (2011)
Klamka, J., Babiarz, A.: Local controllability of semilinear fractional order systems with variable coefficients. In: 20th International Conference on Methods and Models in Automation and Robotics (MMAR 2015), pp. 733–737, August 2015
Klamka, J., Czornik, A., Niezabitowski, M.: Stability and controllability of switched systems. Bull. Polish Acad. Sci. Tech. Sci. 61(3), 547–555 (2013)
Klamka, J., Niezabitowski, M.: Controllability of switched linear dynamical systems. In: 18th International Conference on Methods and Models in Automation and Robotics (MMAR 2013), pp. 464–467, August 2013
Klamka, J., Niezabitowski, M.: Controllability of the fractional discrete linear time-varying infinite-dimensional systems. In: 13th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM). AIP Conference Proceedings, Rhodes, Greece, 23–29 September, pp. 130004(1)–130004(4) (2015)
Klamka, J.: Controllability of Dynamical Systems. Kluwer Academic Publishers, Dordrecht (1991)
Klamka, J.: Controllability of nonlinear discrete systems. Appl. Math. Comput. Sci. 12(2), 173–180 (2002)
Klamka, J.: Local controllability of fractional discrete-time semilinear systems. acta mechanica et automatica 5, 55–58 (2011)
Mozyrska, D., Pawłuszewicz, E.: Controllability of h-difference linear control systems with two fractional orders. Int. J. Syst. Sci. 46(4), 662–669 (2015)
Podlubny, I.: Fractional-order systems and \(pi^{\lambda } d^{\mu }\)-controllers. IEEE Trans. Autom. Control 44(1), 208–214 (1999)
Sikora, B., Klamka, J.: On constrained stochastic controllability of dynamical systems with multiple delays in control. Bull. Polish Acad. Sci. Tech. Sci. 60(2), 301–305 (2012)
Sikora, B.: Controllability of time-delay fractional systems with and without constraints. IET Control Theor. Appl. 10(3), 320–327 (2016)
Tejado, I., Valério, D., Pires, P., Martins, J.: Fractional order human arm dynamics with variability analyses. Mechatronics 23(7), 805–812 (2013)
Acknowledgment
The research presented here was done by first and third author as part of the project funded by the National Science Centre in Poland granted according to decision DEC-2014/13/B/ST7/00755. Moreover, the work of the second author was supported by Polish Ministry for Science and Higher Education under internal grant BKM/506/RAU1/2016 t.1 for Institute of Automatic Control, Silesian University of Technology, Gliwice, Poland. Finally, the calculations were performed with the use of IT infrastructure of GeCONiI Upper Silesian Centre for Computational Science and Engineering (NCBiR grant no POIG.02.03.01-24-099/13).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Babiarz, A., Łęgowski, A., Niezabitowski, M. (2016). Controllability of Positive Discrete-Time Switched Fractional Order Systems for Fixed Switching Sequence. In: Nguyen, NT., Iliadis, L., Manolopoulos, Y., Trawiński, B. (eds) Computational Collective Intelligence. ICCCI 2016. Lecture Notes in Computer Science(), vol 9875. Springer, Cham. https://doi.org/10.1007/978-3-319-45243-2_28
Download citation
DOI: https://doi.org/10.1007/978-3-319-45243-2_28
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-45242-5
Online ISBN: 978-3-319-45243-2
eBook Packages: Computer ScienceComputer Science (R0)