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

International Journal of Applied Mathematics and Computer Science (2005)

- Volume: 15, Issue: 3, page 331-338
- ISSN: 1641-876X

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topOprzędkiewicz, Krzysztof. "An observability problem for a class of uncertain-parameter linear dynamic systems." International Journal of Applied Mathematics and Computer Science 15.3 (2005): 331-338. <http://eudml.org/doc/207747>.

@article{Oprzędkiewicz2005,

abstract = {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.},

author = {Oprzędkiewicz, Krzysztof},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {linear uncertain-parameter dynamic systems; observability},

language = {eng},

number = {3},

pages = {331-338},

title = {An observability problem for a class of uncertain-parameter linear dynamic systems},

url = {http://eudml.org/doc/207747},

volume = {15},

year = {2005},

}

TY - JOUR

AU - Oprzędkiewicz, Krzysztof

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

JO - International Journal of Applied Mathematics and Computer Science

PY - 2005

VL - 15

IS - 3

SP - 331

EP - 338

AB - 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.

LA - eng

KW - linear uncertain-parameter dynamic systems; observability

UR - http://eudml.org/doc/207747

ER -

## References

top- Barnett S. (1992): Matrices. Methods and Applications. - Oxford: Clarendon Press.
- Białas S. (2002): Robust Stability of Polynomials and Matrices. - Cracow: AGH University of Science and Technology Press, (in Polish).
- Busłowicz M. (1997): Stability of Linear Time Invariant Systems with Uncertain Parameters. - Bial ystok: Technical University Press, (in Polish). Zbl0906.34051
- Busłowicz M. (2000): Robust Stability of Dynamic Linear Time InvariantSystems with Delays. - Warsaw-Białystok: Polish Academy of Sciences, The Committee of Automatics and Robotics, (in Polish).
- Feintuch A. (1998): Robust Control Theory in Hilbert Space. - New York: Springer. Zbl0892.93005
- Jakubowska M. (1999): Algorithms for checking stability of the interval matrixand their numerical realization. - Automatyka, Vol. 3, No. 2, pp. 413-430, (in Polish).
- Kalmikov S.A. , Sokin J.I. Juldasev Z. H. (1986): Interval Analysis Methods. - Moscow: Nauka, (in Russian).
- 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).
- Klamka J. (1990): Contollability of Dynamic Systems. - Warsaw: Polish Scientific Publishers, (in Polish).
- Mao X. (2002): Exponential stability of stochastic delay interval systems with Markovian switching. - IEEE Trans. Automat. Contr., Vol. 47, No. 10, pp. 1064-1612.
- Mitkowski W. (1991): Stabilisation of Dynamic Systems. - Warsaw: Polish Scientific Publishers (in Polish).
- Moore R. (1966): Interval Analysis. - Upper Saddle River, Englewood Cliffs: Prentice Hall.
- Moore R. (1997): Methods and Applications of Interval Analysis. - Philadelphia: SIAM.
- Oprzędkiewicz K. (2003): The interval parabolic system. - Arch. Contr. Sci., Vol. 13, No. 4, pp. 391-405. Zbl1151.93368
- 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. Zbl1151.93317

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