Analysis of Positive Linear Continuous–Time Systems Using the Conformable Derivative

Tadeusz Kaczorek

doi:10.2478/amcs-2018-0024

.blurhash-client-img { display: none !important; }

Analysis of Positive Linear Continuous–Time Systems Using the Conformable Derivative

International Journal of Applied Mathematics and Computer Science

Volume 28 (2018): Issue 2 (June 2018)

By: Tadeusz Kaczorek

Open Access

|Jun 2018

Abstract

Positive linear continuous-time systems are analyzed via conformable fractional calculus. A solution to a fractional linear system is derived. Necessary and sufficient conditions for the positivity of linear systems are established. Necessary and sufficient conditions for the asymptotic stability of positive linear systems are also given. The solutions of positive fractional linear systems based on the Caputo and conformable definitions are compared.

References

Abdeljawad, T. (2015). On conformable fractional calculus, Journal of Computational and Applied Mathematics 279: 57-66.10.1016/j.cam.2014.10.016
Search in Google Scholar Back to article
Benvenuti, L. and Farina, L. (2004). A tutorial on the positive realization problem, IEEE Transactions on Automatic Control 49(5): 651-664.10.1109/TAC.2004.826715
Search in Google Scholar Back to article
Farina, L. and Rinaldi, S. (2000). Positive Linear Systems, Theory and Applications, Wiley, New York, NY.10.1002/9781118033029
Search in Google Scholar Back to article
Kaczorek, T. (2016a). Minimal-phase positive electrical circuits, Electrical Review 92(3): 182-189.10.15199/48.2016.03.43
Search in Google Scholar Back to article
Kaczorek, T. (2016b). Positive electrical circuits with zero transfer matrices and their discretization, Computer Applications in Electrical Engineering 14: 1-13.
Search in Google Scholar Back to article
Kaczorek, T. (2015a). A class of positive and stable time-varying electrical circuits, Electrical Review 91(5): 121-124.10.15199/48.2015.05.29
Search in Google Scholar Back to article
Kaczorek, T. (2015b). Normal positive electrical circuits, IET Circuits Theory and Applications 9(5): 691-699.10.1049/iet-cta.2014.0183
Search in Google Scholar Back to article
Kaczorek, T. (2014). Decoupling zeros of positive continuous-time linear systems and electrical circuits, in J. S´wia˛tek et al. (Eds.), Advances in Systems Science, Springer, Cham, pp. 1-15.10.1007/978-3-319-01857-7_1
Search in Google Scholar Back to article
Kaczorek, T. (2013a). Constructability and observability of standard and positive electrical circuits, Electrical Review 89(7): 132-136.
Search in Google Scholar Back to article
Kaczorek, T. (2013b). Positive fractional linear electrical circuits, Proceedings of SPIE 8903, Art. No. 3903-35.10.1117/12.2034370
Search in Google Scholar Back to article
Kaczorek, T. (2013c). Zeroing of state variables in descriptor electrical circuits by state-feedbacks, Electrical Review 89(10): 200-203.
Search in Google Scholar Back to article
Kaczorek, T. (2012). Positive unstable electrical circuits, Electrical Review 88(5a): 187-192.
Search in Google Scholar Back to article
Kaczorek, T. (2011a). Positive electrical circuits and their reachability, Archives of Electrical Engineering 60(3): 283-301.10.2478/v10171-011-0026-3
Search in Google Scholar Back to article
Kaczorek, T. (2011b). Positive systems consisting of n subsystems with different fractional orders, IEEE Transactions on Circuits and Systems 58(6): 1203-1210.10.1109/TCSI.2010.2096111
Search in Google Scholar Back to article
Kaczorek, T. (2011c). Selected Problems of Fractional Systems Theory, Springer, Berlin.10.1007/978-3-642-20502-6
Search in Google Scholar Back to article
Kaczorek, T. (2010). Positive linear systems with different fractional orders, Bulletin of the Polish Academy of Sciences: Technical Sciences 58(3): 453-458.10.2478/v10175-010-0043-1
Search in Google Scholar Back to article
Kaczorek, T. (2002). Positive 1D and 2D Systems, Springer, London.10.1007/978-1-4471-0221-2
Search in Google Scholar Back to article
Kaczorek, T. and Rogowski, K. (2015). Fractional Linear Systems and Electrical Circuits, Studies in Systems, Decision and Control, Vol. 13, Springer, Berlin.10.1007/978-3-319-11361-6
Search in Google Scholar Back to article
Khalil R., Al Horani M., Yousef A., Sababheh M. (2014). A new definition of fractional derivative, Journal of Computational and Applied Mathematics 264: 65-70.10.1016/j.cam.2014.01.002
Search in Google Scholar Back to article