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An observability problem for a class of uncertain-parameter linear dynamic systems

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EN
Abstrakty
EN
An observability problem for a class of linear, uncertain-parameter, time-invariant dynamic SISO systems is discussed. The class of systems under consideration is described by a finite dimensional state-space equation with an interval diagonal state matrix, known control and output matrices and a two-dimensional uncertain parameter space. For the system considered a simple geometric interpretation of the system spectrum can be given. The geometric interpretation of the system spectrum is the base for defining observability and non-observability areas for the discussed system. The duality principle allows us to test observablity using controllability criteria. For the uncertain-parameter system considered, some controllability criteria presented in the author’s previous papers are used. The results are illustrated with numerical examples.
Twórcy
  • AGH University of Science and Technology al. A. Mickiewicza 30, 30–059 Cracow, Poland, kop@uci.agh.edu.pl
Bibliografia
  • [1] Barnett S. (1992): Matrices. Methods and Applications. — Oxford: Clarendon Press.
  • [2] Białas S. (2002): Robust Stability of Polynomials and Matrices. — Cracow: AGH University of Science and Technology Press, (in Polish).
  • [3] Busłowicz M. (1997): Stability of Linear Time Invariant Systems with Uncertain Parameters. — Białystok: Technical University Press, (in Polish).
  • [4] Busłowicz M. (2000): Robust Stability of Dynamic Linear Time Invariant Systems with Delays.—Warsaw-Białystok: Polish Academy of Sciences, The Committee of Automatics and Robotics, (in Polish).
  • [5] Feintuch A. (1998): Robust Control Theory in Hilbert Space. — New York: Springer.
  • [6] Jakubowska M. (1999): Algorithms for checking stability of the interval matrix and their numerical realization. — Automatyka, Vol. 3, No. 2, pp. 413–430, (in Polish).
  • [7] Kalmikov S.A. , Sokin J.I. Juldasev Z. H. (1986): Interval Analysis Methods. —Moscow: Nauka, (in Russian).
  • [8] Kharitonov W. L. (1978): On the asymptotical stability of the equilibrium location for a system of linear differential equations. — Diff. Uravnenya, Vol. 14, No. 11, pp. 2086–2088, (in Russian).
  • [9] Klamka J. (1990): Contollability of Dynamic Systems. — Warsaw: Polish Scientific Publishers, (in Polish).
  • [10] Mao X. (2002): Exponential stability of stochastic delay interval systems with Markovian switching.—IEEE Trans. Automat. Contr., Vol. 47, No. 10, pp. 1064–1612.
  • [11] Mitkowski W. (1991): Stabilisation of Dynamic Systems. — Warsaw: Polish Scientific Publishers (in Polish).
  • [12] Moore R. (1966): Interval Analysis.—Upper Saddle River, Englewood Cliffs: Prentice Hall.
  • [13] Moore R. (1997): Methods and Applications of Interval Analysis. —Philadelphia: SIAM.
  • [14] Oprzędkiewicz K. (2003): The interval parabolic system. — Arch. Contr. Sci., Vol. 13, No. 4, pp. 391–405.
  • [15] Oprzędkiewicz K. (2004): A controllability problem for a class of uncertain-parameters linear dynamic systems. — Arch. Contr. Sci., Vol. 14 (L), No. 1, pp. 85–100.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPZ2-0018-0002
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