Pointwise completeness and pointwise degeneracy of fractional standard and descriptor linear continuous-time systems with different fractional orders

Bingi, K., Ibrahim, R., Karsiti, M.N., Hassam, S.M. and Harindran, V.R. (2019). Frequency response based curve fitting approximation of fractional-order PID controllers, International Journal of Applied Mathematics and Computer Science29(2): 311–326, DOI: 10.2478/amcs-2019-0023.10.2478/amcs-2019-0023Search in Google Scholar

Borawski, K. (2018). Analysis of the positivity of descriptor continuous-time linear systems by the use of Drazin inverse matrix method, in R. Szewczyk et al. (Eds), Automation 2018, Springer, Cham, pp. 172–182.10.1007/978-3-319-77179-3_16Search in Google Scholar

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): 279–284.10.2478/v10175-012-0037-2Search in Google Scholar

Campbell, S.L., Meyer, C.D. and Rose, N.J. (1976). Applications of the Drazin inverse to linear systems of differential equations with singular constant coefficients, SIAM Journal on Applied Mathematics31(3): 411–425.10.1137/0131035Search in Google Scholar

Dai, L. (1989). Singular Control Systems, Springer, Berlin.10.1007/BFb0002475Search in Google Scholar

Djennoune, S., Bettayeb, M. and Al-Saggaf, U.M. (2019). Synchronization of fractional-order discrete-time chaotic systems by an exact delayed state reconstructor: Application to secure communication, International Journal of Applied and Mathematics and Computer Science29(1): 179–194, DOI: 10.2478/amcs-2019-0014.10.2478/amcs-2019-0014Search in Google Scholar

Dzieliński, A., Sierociuk, D. and Sarwas, G. (2009). Ultracapacitor parameters identification based on fractional order model, Proceedings of the European Control Conference, Budapest, Hungary, pp. 196–200.Search in Google Scholar

Fahmy, M.M. and O’Reilly, J. (1989). Matrix pencil of closed-loop descriptor systems: Infinite-eigenvalues assignment, International Journal of Control49(4): 1421–1431.10.1080/00207178908559713Search in Google Scholar

Ferreira, N.M.F. and Machado, J.A.T. (2003). Fractional-order hybrid control of robotic manipulators, 11th International Conference on Advanced Robotics, ICAR, Coimbra, Portugal, pp. 393–398.Search in Google Scholar

Guang-Ren, D. (2010). Analysis and Design of Descriptor Linear Systems, Springer, New York, NY.10.1007/978-1-4419-6397-0_3Search in Google Scholar

Kaczorek, T. (2009). Fractional positive linear systems, Kybernetes: The International Journal of Systems and Cybernetics38(7/8): 1059–1078.10.1108/03684920910976826Search in Google Scholar

Kaczorek, T. (2010). Positive linear systems with different fractional orders, Bulletin of the Polish Academy of Sciences: Technical Sciences58(3): 453–458.10.2478/v10175-010-0043-1Search in Google Scholar

Kaczorek, T. (2011). Selected Problems in Fractional Systems Theory, Springer, Berlin.10.1007/978-3-642-20502-6Search in Google Scholar

Kaczorek, T. (2014). Drazin inverse matrix method for fractional descriptor continuous-time linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences62(3): 409–412.10.2478/bpasts-2014-0042Search in Google Scholar

Kaczorek, T. (2015). Pointwise completeness and pointwise degeneracy of fractional descriptor continuous-time linear systems with regular pencils, Bulletin of the Polish Academy of Sciences: Technical Sciences63(1): 169–172.10.1515/bpasts-2015-0019Search in Google Scholar

Kaczorek, T. (2019). Absolute stability of a class of fractional positive nonlinear systems, International Journal of Applied Mathematics and Computer Science29(1): 93–98, DOI: 10.2478/amcs-2019-0007.10.2478/amcs-2019-0007Search in Google Scholar

Kaczorek, T. (2020). Global stability of positive standard and fractional nonlinear feedback systems, Bulletin of the Polish Academy of Sciences: Technical Sciences68(2): 285–288.Search in Google Scholar

Kaczorek, T. and Busłowicz, M. (2009). Pointwise completeness and pointwise degeneracy of linear continuous-time fractional order systems, Journal of Automation, Mobile Robotics and Intelligent Systems3(1): 8–11.Search in Google Scholar

Kaczorek, T. and Rogowski, K. (2015). Fractional Linear Systems and Electrical Circuits, Springer, Cham.10.1007/978-3-319-11361-6Search in Google Scholar

Korobov, A.A. (2017). On pointwise degenerate linear delay-differential systems with nonnilpotent passive matrices, Journal of Applied and Industrial Mathematics11(3): 369–380.10.1134/S1990478917030085Search in Google Scholar

Kucera, V. and Zagalak, P. (1988). Fundamental theorem of state feedback for singular systems, Automatica24(5): 653–658.10.1016/0005-1098(88)90112-4Search in Google Scholar

Metel’skii, A.V. and Karpuk, V.V. (2009). On properties of pointwise degenerate linear autonomous control systems I, Automation and Remote Control70(10): 1613–1625.10.1134/S0005117909100038Search in Google Scholar

Miller, K.S. and Ross, B. (1993). An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, NY.Search in Google Scholar

Podlubny, I. (1999). Fractional Differential Equations, Academic Press, San Diego, CA.Search in Google Scholar

Sajewski, Ł. (2015). Minimum energy control of fractional positive continuous-time linear systems with two different fractional orders and bounded inputs, in K. Latawiec et al. (Eds), Advances in Modelling and Control of Non-integer-Order Systems, Springer, Cham, pp. 171–181.10.1007/978-3-319-09900-2_16Search in Google Scholar

Sajewski, Ł. (2016). Reachability, observability and minimum energy control of fractional positive continuous-time linear systems with two different fractional orders, Multidimensional Systems and Signal Processing27(1): 27–41.10.1007/s11045-014-0287-2Search in Google Scholar

Trzasko, W. (2014). Pointwise completeness and pointwise degeneracy of linear continuous-time systems with different fractional orders, in R. Szewczyk et al. (Eds), Recent Advances in Automation, Robotics and Measuring Techniques, Springer, Cham, pp. 307–316.10.1007/978-3-319-05353-0_30Search in Google Scholar