Global Stability of Nonlinear Feedback Systems with Fractional Positive Linear Parts

Berman A. and Plemmons R.J. (1994). Nonnegative Matrices in the Mathematical Sciences, SIAM, Philadelphia, MA.10.1137/1.9781611971262Search in Google Scholar

Borawski K. (2017). Modification of the stability and positivity of standard and descriptor linear electrical circuits by state feedbacks, Electrical Review93(11): 176–180.10.15199/48.2017.11.36Search in Google Scholar

Busłowicz M. and Kaczorek T. (2009). Simple conditions for practical stability of positive fractional discrete-time linear systems, International Journal of Applied and Mathematics and Computer Science19(2): 263–269, DOI: 10.2478/v10006-009-0022-6.10.2478/v10006-009-0022-6Search in Google Scholar

Farina L. and Rinaldi S. (2000). Positive Linear Systems: Theory and Applications, Wiley, New York, NY.10.1002/9781118033029Search in Google Scholar

Kaczorek T. (2019a). 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. (2019b). Global stability of nonlinear feedback systems with positive linear parts, International Journal of Nonlinear Sciences and Numerical Simulation20(5): 575–579, DOI: 10.1515/ijnsns-2018-0189.10.1515/ijnsns-2018-0189Search in Google Scholar

Kaczorek T. (2017). Superstabilization of positive linear electrical circuit by state-feedbacks, Bulletin of the Polish Academy of Sciences: Technical Sciences65(5): 703–708.10.1515/bpasts-2017-0075Search in Google Scholar

Kaczorek T. (2016). Analysis of positivity and stability of fractional discrete-time nonlinear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences64(3): 491–494.10.1515/bpasts-2016-0054Search in Google Scholar

Kaczorek T. (2015a). Analysis of positivity and stability of discrete-time and continuous-time nonlinear systems, Computational Problems of Electrical Engineering5(1): 11–16.10.1109/CPEE.2015.7333337Search in Google Scholar

Kaczorek T. (2015b). Stability of fractional positive nonlinear systems, Archives of Control Sciences25(4): 491–496.10.1515/acsc-2015-0031Search in Google Scholar

Kaczorek T. (2012). Positive fractional continuous-time linear systems with singular pencils, Bulletin of the Polish Academy of Sciences: Technical Sciences60(1): 9–12.10.2478/v10175-012-0002-0Search in Google Scholar

Kaczorek T. (2011a). Positive linear systems consisting of n subsystems with different fractional orders, IEEE Transactions on Circuits and Systems58(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. (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. (2002). Positive 1D and 2D Systems, Springer, London.10.1007/978-1-4471-0221-2Search in Google Scholar

Kaczorek T. and Borawski K. (2017). Stability of positive nonlinear systems, 22nd International Conference on Methods and Models in Automation and Robotics, Międzyzdroje, Poland, pp. 564–569, DOI: 10.1109/MMAR.2017.8046890.10.1109/MMAR.2017.8046890Search 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

Kudrewicz J. (1964). Stability of nonlinear systems with feedback, Avtomatika i Telemechanika25(8): 821–837, (in Russian).Search in Google Scholar

Lyapunov A.M. (1963). The General Problem of Motion Stability, Gostechizdat, Moscow, (in Russian).Search in Google Scholar

Leipholz H. (1970). Stability Theory, Academic Press, New York, NY.Search in Google Scholar

Mitkowski W. (2008). Dynamical properties of Metzler systems, Bulletin of the Polish Academy of Sciences: Technical Sciences56(4): 309–312.Search in Google Scholar

Ostalczyk P. (2016). Discrete Fractional Calculus, World Scientific, River Edge, NJ.10.1142/9833Search in Google Scholar

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

Ruszewski A. (2019). Stability conditions for fractional discrete-time state-space systems with delays, 24th International Conference on Methods and Models in Automation and Robotics, Międzyzdroje, Poland, pp. 185–190, DOI: 10.1109/MMAR.2019.8864689.10.1109/MMAR.2019.8864689Search in Google Scholar

Sajewski L. (2017a). Decentralized stabilization of descriptor fractional positive continuous-time linear systems with delays, 22nd International Conference on Methods and Models in Automation and Robotics, Miedzyzdroje, Poland, pp. 482-487.10.1109/MMAR.2017.8046875Search in Google Scholar

Sajewski L. (2017b). Stabilization of positive descriptor fractional discrete-time linear systems with two different fractional orders by decentralized controller, Bulletin of the Polish Academy of Sciences: Technical Sciences65(5): 709–714.10.1515/bpasts-2017-0076Search in Google Scholar