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In the paper a controllability problem for a class of time invariant, discrete linear SISO systems with uncertain parameters is discussed. The system under consideration is described by a finite dimensional state - space equation with an interval diagonal state matrix, an interval control matrix, the know output matrix and the two - dimensional uncertain parameters space. From the considerations shown in the paper it turns out, that the general controllability conditions for the discussed discrete system are the same as for the analogical continuous systemwith uncertain parameters. As an example the controllability problem for an interval parabolic system is discussed, numerical examples are also presented.
Czasopismo
Rocznik
Tom
Strony
161--177
Opis fizyczny
Bibliogr. poz. 17
Twórcy
autor
- University of Mining and Metallurgy, Cracow, Poland, kop@uci.agh.edu.pl
Bibliografia
- [1] S. Barnett: Matrices. Methods and applications. Claredon Press Oxford, 1992.
- [2] S. Bialas: The robust stability of the polynomials and matrices. Ed. UMM, Krakow, 2002, (in Polish).
- [3] M. Buslowicz: Stability of linear time invariant systems with uncertain parameters. Bialystok, 1997, (in Polish).
- [4] M. Buslowicz: The robust stability of the dynamic linear time invariant systems with delays. Eds Comitee for Automatics and Robotics of Polish Academy of Sciences, Warsaw-Bialystok, 2000, (in Polish).
- [5] A. Feintuch: Robust Control Theory in Hilbert Space. Springer, 1998.
- [6] J. Jakubowska: Algorithms for checking stability of the interval matrix and their numerical realization. Automatyka, 3(2), (1999), 413-430, (in Polish).
- [7] S. A. Kalmikov, J. I. Sokin and Z. H. Juldasev: Metody intervalnogo analiza. Nauka, 1986, (in Russian).
- [8] W. L. Kharitonov: Ob assimptoticeskoj ustojcivosti polozenija ravnovesija semejstva sistem liniejnych differencialnych uravnenij. Diff. Uravnienija, 14(11), (1978), 2086-2088, (in Russian).
- [9] J. Klamka: Controllability of Dynamical Systems. Kluwer Academic Publishers, Dordrecht, The Nederlands, 1991.
- [10] X. Mao: Exponential Stability of Stochastic Delay Interval Systems With Markovian Switching. IEEE Trans. Aut. Cont., 47(10), (2002), 1064-1612.
- [11] W. Mitkowski: Stabilisation of the dynamic systems. PWN,Warszawa, 1991, (in Polish).
- [12] R. Moore: Interval Analysis. Prentice Hall, 1966.
- [13] R. Moore: Methods and Applications of Interval Analysis. SIAM, Philadelphia, 1979.
- [14] K. Oprzedkiewicz: The interval parabolic system. Archives of Control Sciences, 13(4), (2003), 415-430.
- [15] K. Oprzedkiewicz: A controllability problem for a class of uncertain – parameters linear dynamic systems. Archives of Control Sciences, 14(1), (2004), 85-100.
- [16] Y. Smagina and I. Brewer: Using interval arithmetic for robust state feedback design. System and Control Letters, 46 (2002), 187-194.
- [17] T. Tsuino and Fuji K. Wei: On the connection between controllability and stabilizability of linear systems with structural uncertain parameters. Automatica, 29(1), (1993), 7-12.
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Bibliografia
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bwmeta1.element.baztech-article-BSW3-0009-0010