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ISSN 2083-6473
ISSN 2083-6481 (electronic version)
Editor-in-Chief
Associate Editor
Prof. Tomasz Neumann
Published by
TransNav, Faculty of Navigation
Gdynia Maritime University
3, John Paul II Avenue
81-345 Gdynia, POLAND
e-mail transnav@umg.edu.pl
Stability Tests of Positive Fractional Continuous-time Linear Systems with Delays
1 Bialystok University of Technology, Białystok, Poland
ABSTRACT: Necessary and sufficient conditions for the asymptotic stability of positive fractional continuous-time linear systems with many 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.
KEYWORDS: Consequences of Delays, Stability Tests, Asymptotic Stability, Positive Fractional System, Positive Fractional Continuous-Time Linear System, Linear System, Positive Standard Linear System, Delay
REFERENCES
Busłowicz 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. Vol. 55, No. 1, 2007, 347-350.
Busłowicz M., Simple stability conditions for linear positive discrete-time systems with delays, Bull. Pol. Acad. Techn. Sci. Vol. 50, No. 4, 2008.
Busłowicz M., Robust stability of dynamical linear stationary systems with delays, Publishing Department of Technical University of Białystok, Warszawa-Białystok 2000, (in Polish).
Busłowicz M., Robust stability of scalar positive discrete-time linear systems with delays, Proc. Int. Conf. on Power Electronics and Intelligent Control, Warszawa 2005, Paper 163 (on CD-ROM).
Busłowicz M., Stability of positive singular discrete-time system with unit delay with canonical forms of state matrices, Proc. 12th IEEE int. Conf. on Methods and Models in Automation and Robotics, Międzyzdroje 2006, pp. 215-218.
Bysłowicz 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., Vol. 52, No. 2, 2004, pp. 99-102.
Busłowicz M. and Kaczorek T., Robust stability of positive discrete-time interval systems with time-delays, Bull. of Pol. Acad. of Sci., Tech. Sci., Vol. 55, No. 1, 2007, pp. 1-5.
Busłowicz M. and Kaczorek T., Stability and robust stability of positive discrete-time systems with pure delays, Proc. of the 10th IEEE Int. Conf. on Methods and Models in Automation and Robotics, Międzyzdroje 2004, Vol. 1, pp.105-108.
Busłowicz M. and Kaczorek T., Robust stability of positive discrete-time systems with pure delays with linear unit rank uncertainty structure, Proc. of the 11th IEEE Int. Conf. on Methods and Models in Automation and Robotics, Międzyzdroje 2005, Paper 0169 (on CD-ROM).
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. and 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. and Son N.K., Stability radii of positive higher order difference systems, System & Control Letters, Vol. 49, 2003, pp.377-388.
Hmamed A., Benzaouia A., Ait Rami M. and Tadeo F. Positive stabilization of discrete-time systems with unknown delays and bounded control, Proc. European Control Conference, Kos, Greece, Jul 2007, 5616-5622 (paper ThD07.3).
Kaczorek T., Positive 1D and 2D Systems, Springer-Verlag, London 2002.
Kaczorek T., “Stability of positive continuous-time linear systems with delays”, Bul. Pol. Acad. Sci. Techn. vol. 57. no. 4, 2009, 395-398.
Kaczorek T., Stability of positive discrete-time systems with time-delays, Proc. 8th World Multiconference on Systemics, Cybernetics and Informatics, Orlando Florida USA, July 2004, pp.321-324.
Kaczorek T., Choice of the forms of Lyapunov functions for positive 2D Roesser model, Int. J. Applied Math. And Comp. Sci. Vol. 17 (2007), No. 4, pp.471-475.
Kaczorek T., Asymptotic stability of positive 1D and 2D linear systems, Recent Advances in Control and Automation, Academ. Publ. House EXIT 2008, pp.41-52.
Kaczorek T., Practical stability of positive fractional discrete-time linear systems, Bull. Pol. Acad. Techn. Sci. Vol. 56, No. 4.
Kaczorek T., New stability tests of positive standard and fractional systems, Circuits and Systems 2011 (in press).
Narendra K.S. and Shorten R., “Hurwitz stability of Metzler matrices”, IEEE Trans. Autom. Contr. vol. 55, no. 6 June 2010, 1484-1487.
Niculescu S.-I., Delay effects on stability. A robust control approach, Springer-Verlag, London 2001.
Twardy M., On the alternative stability criteria for positive systems, Bull. Pol. Acad. Techn. Sci. Vol. 55, 2007, No. 4, pp.385-303.
Citation note:
Kaczorek T.: Stability Tests of Positive Fractional Continuous-time Linear Systems with Delays. TransNav, the International Journal on Marine Navigation and Safety of Sea Transportation, Vol. 7, No. 2, doi:10.12716/1001.07.02.08, pp. 211-215, 2013
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