Global Stability of Discrete–Time Feedback Nonlinear Systems with Descriptor Positive Linear Parts and Interval State Matrices
References
- Berman, A. and Plemmons, R. (1994). Nonnegative Matrices in the Mathematical Sciences, SIAM, Philadelphia.10.1137/1.9781611971262
- Borawski, K. (2017). Modification of the stability and positivity of standard and descriptor linear electrical circuits by state feedbacks, Electrical Review 93(11): 176–180.10.15199/48.2017.11.36
- Dai, L. (1989). Singular Control Systems, Springer, Berlin.10.1007/BFb0002475
- Farina, L. and Rinaldi, S. (2000). Positive Linear Systems: Theory and Applications, Wiley, New York.10.1002/9781118033029
- Gluck, J. and Mironchenko, A. (2020). Stability criteria for positive linear discrete-time systems, arXiv 2011.02251.
- Kaczorek, T. (2011). Selected Problems of Fractional System Theory, Springer, Berlin.10.1007/978-3-642-20502-6
- Kaczorek, T. (2019a). Absolute stability of a class of fractional positive nonlinear systems, International Journal of Applied Mathematics and Computer Science 29(1): 93–98, DOI: 10.2478/amcs-2019-0007.10.2478/amcs-2019-0007
- Kaczorek, T. (2019b). Global stability of nonlinear feedback systems with positive linear parts, International Journal of Nonlinear Sciences and Numerical Simulation 20(5): 575–579.10.1515/ijnsns-2018-0189
- Kaczorek, T. (2020). Global stability of positive standard and fractional nonlinear feedback systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 68(2): 285–288.
- Kaczorek, T. (2021). New sufficient conditions of global stability of nonlinear positive electrical circuits, in R. Szewczyk et al. (Eds), Recent Achievements in Automation, Robotics and Measurement Techniques: Automation 2021, Springer, Cham, pp. 3–9.10.1007/978-3-030-74893-7_1
- Kaczorek, T. and Rogowski, K. (2015). Fractional Linear Systems and Electrical Circuits, Springer, New York.10.1007/978-3-319-11361-6
- Kharitonov, V. (1978). Asymptotic stability of an equilibrium position of a family of systems of linear differential equations, Differentsialnye Uravneniya 14(11): 2086–2088, (in Russian).
- Leipholz, H. (1970). Stability Theory, Academic Press, New York.
- Lyapunov, A. (1963). General Problem of Stable Movement, Gostechizdat, Moscow, (in Russian).
- Rami, M. and Napp, D. (2012). Characterization and stability of autonomous positive descriptor systems, IEEE Transactions on Automatic Control 57(10): 2668–2673.10.1109/TAC.2012.2190211
- Sajewski, Ł. (2017). 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 Sciences 65(5): 709–714.10.1515/bpasts-2017-0076
- Si, X., Yang, H. and Ivanov, I.G. (2021). Conditions and a computation method of the constrained regulation problem for a class of fractional-order nonlinear continuous-time systems, International Journal of Applied Mathematics and Computer Science 31(1): 17–28, DOI: 10.34768/amcs-2021-0002.
- Virnik, E. (2008). Stability analysis of positive descriptor systems, Linear Algebra and Its Applications 429(10): 2640–2659.10.1016/j.laa.2008.03.002
Language: English
Page range: 5 - 10
Submitted on: Apr 21, 2021
Accepted on: Dec 5, 2021
Published on: Mar 31, 2022
Published by: Sciendo
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© 2022 Tadeusz Kaczorek, Andrzej Ruszewski, published by Sciendo
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