Abstract
Necessary and sufficient conditions for the asymptotic stability of positive fractional continuous-time linear systems with delays are established. It is shown that: 1) the asymptotic stability of the positive fractional system is independent of their delays, 2) the checking of the asymptotic stability of the positive fractional systems with delays can be reduced to checking of the asymptotic stability of positive standard linear systems without delays.
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References
Buslowicz, M.: Robust stability of positive discrete-time linear systems with multiple delays with unity rank uncertainty structure or non-negative perturbation matrices. Bull. Pol. Acad. Techn. Sci. 55(1), 347–350 (2007)
Buslowicz, M.: Simple stability conditions for linear positive discrete-time systems with delays. Bull. Pol. Acad. Techn. Sci. 50(4) (2008)
Buslowicz, M.: Robust stability of dynamical linear stationary systems with delays. Publishing Department of Technical University of Bialystok, Warszawa-Bialystok (2000) (in Polish)
Buslowicz, M.: Robust stability of scalar positive discrete-time linear systems with delays. In: Proc. Int. Conf. on Power Electronics and Intelligent Control, Warszawa, Paper 163, on CD-ROM (2005)
Buslowicz, M.: Stability of positive singular discrete-time system with unit delay with canonical forms of state matrices. In: Proc. 12th IEEE Int. Conf. on Methods and Models in Automation and Robotics, Miedzyzdroje, pp. 215–218 (2006)
Buslowicz, M.: Robust stability of positive discrete-time linear systems with multiple delays with linear unit rank uncertainty structure or non-negative perturbation matrices. Bull. of Pol. Acad. of Sci., Tech. Sci. 52(2), 99–102 (2004)
Buslowicz, M., Kaczorek, T.: Robust stability of positive discrete-time interval systems with time-delays. Bull. of Pol. Acad. of Sci., Tech. Sci. 55(1), 1–5 (2007)
Buslowicz, M., Kaczorek, T.: Stability and robust stability of positive discrete-time systems with pure delays. In: Proc. of the 10th IEEE Int. Conf. on Methods and Models in Automation and Robotics, Miedzyzdroje, vol. 1, pp. 105–108 (2004)
Buslowicz, M., Kaczorek, T.: Robust stability of positive discrete-time systems with pure delays with linear unit rank uncertainty structure. In: Proc. of the 11th IEEE Int. Conf. on Methods and Models in Automation and Robotics, Miedzyzdroje, Paper 0169, on CD-ROM (2005)
Farina, L., Rinaldi, S.: Positive linear systems; Theory and applications. J. Wiley, New York (2000)
Górecki, H.: Analysis and synthesis of control systems with delays. WNT, Warszawa (1971) (in Polish)
Górecki, H., Fuksa, S., Grabowski, P., Korytowski, A.: Analysis and synthesis of time delay systems. PWN-J. Willey, Warszawa - Chichester (1989)
Górecki, H., Korytowski, A.: Advances in optimizations and stability analysis of dynamical systems. Publishing Department of University Mining and Metallurgy, Kraków (1993)
Hinrichsen, D., Hgoc, P.H.A., Son, N.K.: Stability radii of positive higher order difference systems. System & Control Letters 49, 377–388 (2003)
Hmamed, A., Benzaouia, A., Ait Rami, M., Tadeo, F.: Positive stabilization of discrete-time systems with unknown delays and bounded control. In: Proc. European Control Conference, Kos, Greece, pp. 5616–5622, paper ThD07.3 (July 2007)
Kaczorek, T.: Positive 1D and 2D Systems. Springer, London (2002)
Kaczorek, T.: Stability of positive continuous-time linear systems with delays. Bul. Pol. Acad. Sci. Techn. 57(4), 395–398 (2009)
Kaczorek, T.: Stability of positive discrete-time systems with time-delays. In: Proc. 8th World Multiconference on Systemics, Cybernetics and Informatics, Orlando Florida, USA, pp. 321–324 (July 2004)
Kaczorek, T.: Choice of the forms of Lyapunov functions for positive 2D Roesser model. Int. J. Applied Math. And Comp. Sci. 17(4), 471–475 (2007)
Kaczorek, T.: Asymptotic stability of positive 1D and 2D linear systems. In: Recent Advances in Control and Automation, pp. 41–52. Academ. Publ. House EXIT (2008)
Kaczorek, T.: Practical stability of positive fractional discrete-time linear systems. Bull. Pol. Acad. Techn. Sci. 56(4), 313–317 (2008)
Narendra, K.S., Shorten, R.: Hurwitz stability of Metzler matrices. IEEE Trans. Autom. Contr. 55(6), 1484–1487 (2010)
Niculescu, S.-I.: Delay effects on stability. A robust control approach. Springer, London (2001)
Twardy, M.: On the alternative stability criteria for positive systems. Bull. Pol. Acad. Techn. Sci. 55(4), 303–385 (2007)
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Kaczorek, T. (2011). Stability of Positive Fractional Continuous-Time Linear Systems with Delays. In: Dobnikar, A., Lotrič, U., Šter, B. (eds) Adaptive and Natural Computing Algorithms. ICANNGA 2011. Lecture Notes in Computer Science, vol 6594. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20267-4_32
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DOI: https://doi.org/10.1007/978-3-642-20267-4_32
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