Robust stability of positive continuous-time linear systems with delays

Mikołaj Busłowicz

International Journal of Applied Mathematics and Computer Science (2010)

  • Volume: 20, Issue: 4, page 665-670
  • ISSN: 1641-876X

Abstract

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The paper is devoted to the problem of robust stability of positive continuous-time linear systems with delays with structured perturbations of state matrices. Simple necessary and sufficient conditions for robust stability in the general case and in the case of systems with a linear uncertainty structure in two sub-cases: (i) a unity rank uncertainty structure and (ii) nonnegative perturbation matrices are established. The problems are illustrated with numerical examples.

How to cite

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Mikołaj Busłowicz. "Robust stability of positive continuous-time linear systems with delays." International Journal of Applied Mathematics and Computer Science 20.4 (2010): 665-670. <http://eudml.org/doc/208015>.

@article{MikołajBusłowicz2010,
abstract = {The paper is devoted to the problem of robust stability of positive continuous-time linear systems with delays with structured perturbations of state matrices. Simple necessary and sufficient conditions for robust stability in the general case and in the case of systems with a linear uncertainty structure in two sub-cases: (i) a unity rank uncertainty structure and (ii) nonnegative perturbation matrices are established. The problems are illustrated with numerical examples.},
author = {Mikołaj Busłowicz},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {positive continuous-time linear system; delays; robust stability; linear uncertainty; interval system},
language = {eng},
number = {4},
pages = {665-670},
title = {Robust stability of positive continuous-time linear systems with delays},
url = {http://eudml.org/doc/208015},
volume = {20},
year = {2010},
}

TY - JOUR
AU - Mikołaj Busłowicz
TI - Robust stability of positive continuous-time linear systems with delays
JO - International Journal of Applied Mathematics and Computer Science
PY - 2010
VL - 20
IS - 4
SP - 665
EP - 670
AB - The paper is devoted to the problem of robust stability of positive continuous-time linear systems with delays with structured perturbations of state matrices. Simple necessary and sufficient conditions for robust stability in the general case and in the case of systems with a linear uncertainty structure in two sub-cases: (i) a unity rank uncertainty structure and (ii) nonnegative perturbation matrices are established. The problems are illustrated with numerical examples.
LA - eng
KW - positive continuous-time linear system; delays; robust stability; linear uncertainty; interval system
UR - http://eudml.org/doc/208015
ER -

References

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  1. Bhattacharyya, S.P., Chapellat, H. and Keel, L.H. (1995). Robust Control: The Parametric Approach, Prentice Hall, New York, NY. Zbl0838.93008
  2. Busłowicz, M. (2000). Robust Stability of Dynamical Linear Stationary Systems with Delays, Publishing Department of the Technical University of Białystok, Białystok, (in Polish). 
  3. Busłowicz, M. (2008a). Simple stability conditions for linear positive discrete-time systems with delays, Bulletin of the Polish Academy of Sciences: Technical Sciences 56(4): 325-328. 
  4. Busłowicz, M. (2008b). Simple conditions for robust stability of linear positive discrete-time systems with one delay, Journal of Automation, Mobile Robotics and Intelligent Systems 2(2): 18-22. 
  5. Farina, L. and Rinaldi, S. (2000). Positive Linear Systems; Theory and Applications, J. Wiley, New York, NY. Zbl0988.93002
  6. Górecki, H. and Korytowski, A. (Eds.) (1993). Advances in Optimization and Stability Analysis of Dynamical Systems, Publishing Department of the University of Mining and Metallurgy, Cracow. Zbl0737.93026
  7. Gu, K., Kharitonov, K.L. and Chen, J. (2003). Stability of TimeDelay Systems, Birkhäuser, Boston, MA. 
  8. Gu, K. and Niculescu, S.I. (2006). Stability Analysis of Timedelay Systems: A Lyapunov Approach, Springer-Verlag, London. 
  9. Hmamed, A., Benzaouia, A., Rami, M.A. and Tadeo, F. (2007). Positive stabilization of discrete-time systems with unknown delay and bounded controls, Proceedings of the European Control Conference, Kos, Greece, pp. 5616-5622, (paper ThD07.3). 
  10. Kaczorek, T. (2002). Positive 1D and 2D Systems, Springer-Verlag, London. Zbl1005.68175
  11. Kaczorek, T. (2009). Stability of positive continuous-time linear systems with delays, Bulletin of the Polish Academy of Sciences: Technical Sciences 57(4): 395-398. 
  12. Niculescu, S.-I. (2001). Delay Effects on Stability. A Robust Control Approach, Springer-Verlag, London. 
  13. Rami, M.A., Helmke, U. and Tadeo, F. (2007). Positive observation problem for linear positive systems, Proceedings of the Mediterranean Conference on Control and Automation, Athens, Greece, (paper T19-027). 
  14. Wu, M., He.Y., She J.-A., and Liu G.-P. (2004). Delay-dependent criteria for robust stability of time-varying delay systems, Automatica 40(8): 1435-1439. Zbl1059.93108

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