Reduced–Order Perfect Nonlinear Observers of Fractional Descriptor Discrete–Time Nonlinear Systems

Cuihong, W. (2012). New delay-dependent stability criteria for descriptor systems with interval time delay, Asian Journal of Control 14(1): 197-206.10.1002/asjc.287Search in Google Scholar

Dodig, M. and Stosic, M. (2009). Singular systems state feedbacks problems, Linear Algebra and Its Applications 431(8): 1267-1292.10.1016/j.laa.2009.04.024Search in Google Scholar

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

Duan, G.R. (2010). Analysis and Design of Descriptor Linear Systems, Springer, New York, NY.10.1007/978-1-4419-6397-0Search in Google Scholar

Fahmy, M.M. and O’Reill, J. (1989). Matrix pencil of closed-loop descriptor systems: Infinite-eigenvalues assignment, International Journal of Control 49(4): 1421-1431.10.1080/00207178908559713Search in Google Scholar

Gantmacher, F.R. (1959). The Theory of Matrices, Chelsea, London.Search in Google Scholar

Kaczorek, T. (1992). Linear Control Systems, Wiley, New York, NY.Search in Google Scholar

Kaczorek, T. (2001). Full-order perfect observers for continuous-time linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 49(4): 549-558.Search in Google Scholar

Kaczorek, T. (2004). Infinite eigenvalue assignment by an output feedback for singular systems, International Journal of Applied Mathematics and Computer Science 14(1): 19-23.Search in Google Scholar

Kaczorek, T. (2008). Fractional positive continuous-time linear systems and their reachability, International Journal of Applied Mathematics and Computer Science 18(2): 223-228, DOI: 10.2478/v10006-008-0020-0.10.2478/v10006-008-0020-0Search in Google Scholar

Kaczorek, T. (2011a). Positive linear systems consisting of n subsystems with different fractional orders, IEEE Transaction on Circuits and Systems 58(7): 1203-1210.10.1109/TCSI.2010.2096111Search in Google Scholar

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

Kaczorek, T. (2012a). Checking of the positivity of descriptor linear systems with singular pencils, Archives of Control Sciences 22(1): 77-86.10.2478/v10170-011-0013-3Search in Google Scholar

Kaczorek T. (2012b). Positive fractional continuous-time linear systems with singular pencils, Bulletin of the Polish Academy of Sciences: Technical Sciences 60(1): 9-12.10.2478/v10175-012-0002-0Search in Google Scholar

Kaczorek, T. (2013). Descriptor fractional linear systems with regular pencils, Asian Journal of Control 15(4): 1051-1064.10.1002/asjc.579Search in Google Scholar

Kaczorek, T. (2014a). Fractional descriptor observers for fractional descriptor continuous-time linear systems, Archives of Control Sciences 24(1): 27-37.10.2478/acsc-2014-0002Search in Google Scholar

Kaczorek, T. (2014b). Reduced-order fractional descriptor observers for fractional descriptor continuous-time linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 62(4): 889-895.10.2478/bpasts-2014-0098Search in Google Scholar

Kaczorek, T. (2015). Perfect observers of fractional descriptor continuous-time linear systems, in K. Latawiec, et al. (Eds.), Advances in Modeling and Control of Non-integer Orders Systems, Springer, Cham, pp. 3-12.10.1007/978-3-319-09900-2_1Search in Google Scholar

Kaczorek, T. (2016a). Perfect nonlinear observers of descriptor discrete-time nonlinear systems, Asian Journal of Control, (submitted).10.1515/fca-2016-0041Search in Google Scholar

Kaczorek, T. (2016b). Perfect nonlinear observers of fractional descriptor continuous-time nonlinear systems, Fractional Calculus and Applied Analysis 19(3): 775-784.10.1515/fca-2016-0041Search in Google Scholar

Kaczorek, T. (2016c). Positivity and stability of fractional descriptor time-varying discrete-time linear systems, International Journal of Applied Mathematics and Computer Science 26(1): 5-13, DOI: 10.1515/amcs-2016-0001.10.1515/amcs-2016-0001Search in Google Scholar

Kaczorek, T. (2016d). Reduced-order fractional descriptor observers for a class of fractional descriptor continuous-time nonlinear systems, International Journal of Applied Mathematics and Computer Science 26(2): 277-283, DOI: 10.1515/amcs-2016-0019.10.1515/amcs-2016-0019Search in Google Scholar

Kociszewski, R. (2013). Observer synthesis for linear discrete-time systems with different fractional orders, Pomiary Automatyka Robotyka 17(2): 376-381.Search in Google Scholar

Kucera, V. and Zagalak, P. (1988). Fundamental theorem of state feedback for singular systems, Automatica 24(5): 653-658.10.1016/0005-1098(88)90112-4Search in Google Scholar

Lewis, F.L. (1983). Descriptor systems, expanded descriptor equation and Markov parameters, IEEE Transactions on Automatic Control 28(5): 623-627.10.1109/TAC.1983.1103285Search in Google Scholar

Luenberger, D.G. (1977). Dynamical equations in descriptor form, IEEE Transactions on Automatic Control 22(3): 312-321.10.1109/TAC.1977.1101502Search in Google Scholar

Luenberger, D.G. (1978). Time-invariant descriptor systems, Automatica 14(5): 473-480.10.1016/0005-1098(78)90006-7Search in Google Scholar

N’Doye, I., Darouach, M., Voos, H. and Zasadzinski, M. (2013). Design of unknown input fractional-order observers for fractional-order systems, International Journal of Applied Mathematics and Computer Science 23(3): 491-500, DOI: 10.2478/amcs-2013-0037.10.2478/amcs-2013-0037Search in Google Scholar

Oldham, K.B. and Spanier, J. (1974). The Fractional Calculus, Academic Press, New York, NY.Search in Google Scholar

Ostalczyk, P. (2008). Epitome of the Fractional Calculus: Theory and Its Applications in Automatics, Ł´od´z University of Technology Publishing House, Ł´od´z, (in Polish).Search in Google Scholar

Podlubny, I. (1999). Fractional Differential Equations, Academic Press, New York, NY.Search in Google Scholar

Sajewski, Ł (2016). Descriptor fractional discrete-time linear system with two different fractional orders and its solution, Bulletin of the Polish Academy of Sciences: Technical Sciences 64(1): 15-20.10.1515/bpasts-2016-0003Search in Google Scholar

Van Dooren, P. (1979). The computation of Kronecker’s canonical form of a singular pencil, Linear Algebra and Its Applications 27: 103-140.10.1016/0024-3795(79)90035-1Search in Google Scholar

Vinagre, B.M., Monje, C.A. and Calderon, A.J. (2002). Fractional order systems and fractional order control actions, IEEE Conference on Decision and Control, Las Vegas, NV, USA, pp. 2550-2554.Search in Google Scholar

Virnik, E. (2008). Stability analysis of positive descriptor systems, Linear Algebra and Its Applications 429(10): 2640-2659.10.1016/j.laa.2008.03.002Search in Google Scholar