Robust stability of positive continuous-time linear systems with delays

• Autorzy: Mikołaj Busłowicz
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

positive continuous-time linear system; delays; robust stability; linear uncertainty; interval system

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2010
• Tom: 20
• Numer: 4
• Strony: 665-670

Daty

wydano

2010

otrzymano

2010-02-12

poprawiono

2010-05-31

Twórcy

autor

Mikołaj Busłowicz

• Faculty of Electrical Engineering, Białystok University of Technology, ul. Wiejska 45D, 15-351 Białystok, Poland

Bibliografia

• Bhattacharyya, S.P., Chapellat, H. and Keel, L.H. (1995). Robust Control: The Parametric Approach, Prentice Hall, New York, NY.
• Busłowicz, M. (2000). Robust Stability of Dynamical Linear Stationary Systems with Delays, Publishing Department of the Technical University of Białystok, Białystok, (in Polish).
• 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.
• 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.
• Farina, L. and Rinaldi, S. (2000). Positive Linear Systems; Theory and Applications, J. Wiley, New York, NY.
• 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.
• Gu, K., Kharitonov, K.L. and Chen, J. (2003). Stability of TimeDelay Systems, Birkhäuser, Boston, MA.
• Gu, K. and Niculescu, S.I. (2006). Stability Analysis of Timedelay Systems: A Lyapunov Approach, Springer-Verlag, London.
• 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).
• Kaczorek, T. (2002). Positive 1D and 2D Systems, Springer-Verlag, London.
• 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.
• Niculescu, S.-I. (2001). Delay Effects on Stability. A Robust Control Approach, Springer-Verlag, London.
• 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).
• 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.

Identyfikatory

DOI

10.2478/v10006-010-0049-8