Stability of Interval Positive Fractional Discrete–Time Linear Systems

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

Busłowicz, M. (2008). Stability of linear continuous-time fractional order systems with delays of the retarded type, Bulletin of the Polish Academy of Sciences: Technical Sciences 56(4): 319-324.Search 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 Sciences 60(2): 279-284.10.2478/v10175-012-0037-2Search 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 Mathematics and Computer Science 19(2): 263-269, DOI: 10.2478/v10006-009-0022-6.10.2478/v10006-009-0022-6Open DOISearch 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. (1997). Positive singular discrete-time linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 45(4): 619-631.Search 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. (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/v10006-008-0020-0Open DOISearch in Google Scholar

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/v10175-010-0043-1Search in Google Scholar

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

Kaczorek, T. (2012a). Selected Problems of Fractional Systems Theory, Springer, Berlin.10.1007/978-3-642-20502-6Search 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). Application of the Drazin inverse to the analysis of descriptor fractional discrete-time linear systems with regular pencils, International Journal of Applied Mathematics and Computer Science 23(1): 29-33, DOI: 10.2478/amcs-2013-0003.10.2478/amcs-2013-0003Open DOISearch in Google Scholar

Kaczorek, T. (2014). Descriptor positive discrete-time and continuous-time nonlinear systems, in R.S. Romaniuk (Ed.), Photonics Applications in Astronomy, Communications, Industry, and High-Energy Physics Experiments, Proceedings of SPIE, Vol. 9290, SPIE, Cardiff, pp. 1-11.10.1117/12.2074558Search in Google Scholar

Kaczorek, T. (2015a). Positivity and stability of discrete-time nonlinear systems, IEEE 2nd International Conference on Cybernetics, Gdynia, Poland, pp. 156-159.10.1109/CYBConf.2015.7175924Search in Google Scholar

Kaczorek, T. (2015b). Analysis of positivity and stability of discrete-time and continuous-time nonlinear systems, Computational Problems of Electrical Engineering 5(1): 11-16.10.1109/CPEE.2015.7333337Search in Google Scholar

Kaczorek, T. (2015c). Stability of fractional positive nonlinear systems, Archives of Control Sciences 25(4): 491-496.10.1515/acsc-2015-0031Search 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 Sciences 64(3): 491-494.10.1515/bpasts-2016-0054Search in Google Scholar

Kaczorek, T. (2018a). Positivity and stability of standard and fractional descriptor continuous-time linear and nonlinear systems, International Journal of Nonlinear Sciences and Numerical Simulation, (in press).10.1515/ijnsns-2017-0049Search in Google Scholar

Kaczorek, T. (2018b). Stability of interval positive continuous-time linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 66(1): 31-35.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

Kharitonov, V.L. (1978). Asymptotic stability of an equilibrium position of a family of systems of differential equations, Differentsial’nye uravneniya 14(11): 2086-2088.Search in Google Scholar

Ortigueira, M. D. (2011). Fractional Calculus for Scientists and Engineers, Springer, Dordrecht.10.1007/978-94-007-0747-4Search 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, Publishing House of the Łód´z University of Technology, Łód´z, (in Polish).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

Radwan, A.G., Soliman, A.M., Elwakil, A.S. and Sedeek A. (2009). On the stability of linear systems with fractional-order elements. Chaos, Solitones and Fractals 40(5): 2317-2328.10.1016/j.chaos.2007.10.033Search in Google Scholar

Sajewski, Ł (2016a). Descriptor fractional discrete-time linear system and its solution-comparison of three different methods, in R. Szewczyk et al. (Eds.), Challenges in Automation, Robotics and Measurement Techniques, Springer, Cham, pp. 37-50.10.1007/978-3-319-29357-8_4Search in Google Scholar

Sajewski, Ł. (2016b). 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

Solteiro Pires, E.J., Tenreiro Machado, J.A. and de Moura Oliveira, P.B. (2006). Fractional dynamics in genetic algorithms, IFAC Proceedings Volumes 39(11): 414-419.10.3182/20060719-3-PT-4902.00070Search in Google Scholar

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

Xiang-Jun, W., Zheng-Mao, W. and Jun-Guo, L. (2008). Stability analysis of a class of nonlinear fractional-order systems, IEEE Transactions on Circuits and Systems II: Express Briefs 55(11): 1178-1182.10.1109/TCSII.2008.2002571Search in Google Scholar