Uniform exponential stability for linear discrete time systems with stochastic perturbations in Hilbert spaces

Viorica Mariela Ungureanu

Bollettino dell'Unione Matematica Italiana (2004)

  • Volume: 7-B, Issue: 3, page 757-772
  • ISSN: 0392-4041

Abstract

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In this paper we study the exponential and uniform exponential stability problem for linear discrete time-varying systems with independent stochastic perturbations. We give two representations of the solutions of the discussed systems and we use them to obtain necessary and sufficient conditions for the two types of stability. A deterministic characterization of the uniform exponential stability, in terms of Lyapunov equations are given.

How to cite

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Ungureanu, Viorica Mariela. "Uniform exponential stability for linear discrete time systems with stochastic perturbations in Hilbert spaces." Bollettino dell'Unione Matematica Italiana 7-B.3 (2004): 757-772. <http://eudml.org/doc/195495>.

@article{Ungureanu2004,
abstract = {In this paper we study the exponential and uniform exponential stability problem for linear discrete time-varying systems with independent stochastic perturbations. We give two representations of the solutions of the discussed systems and we use them to obtain necessary and sufficient conditions for the two types of stability. A deterministic characterization of the uniform exponential stability, in terms of Lyapunov equations are given.},
author = {Ungureanu, Viorica Mariela},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {757-772},
publisher = {Unione Matematica Italiana},
title = {Uniform exponential stability for linear discrete time systems with stochastic perturbations in Hilbert spaces},
url = {http://eudml.org/doc/195495},
volume = {7-B},
year = {2004},
}

TY - JOUR
AU - Ungureanu, Viorica Mariela
TI - Uniform exponential stability for linear discrete time systems with stochastic perturbations in Hilbert spaces
JO - Bollettino dell'Unione Matematica Italiana
DA - 2004/10//
PB - Unione Matematica Italiana
VL - 7-B
IS - 3
SP - 757
EP - 772
AB - In this paper we study the exponential and uniform exponential stability problem for linear discrete time-varying systems with independent stochastic perturbations. We give two representations of the solutions of the discussed systems and we use them to obtain necessary and sufficient conditions for the two types of stability. A deterministic characterization of the uniform exponential stability, in terms of Lyapunov equations are given.
LA - eng
UR - http://eudml.org/doc/195495
ER -

References

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  2. DA PRATO, G.- ZABCZYC, J., Stochastic Equations in Infinite Dimensions, University PressCambridge, 1992. Zbl0761.60052MR1207136
  3. DOUGLAS, R., Banach algebra Techniques in Operator Theory, Academic Press, New York and London, 1972. Zbl0247.47001MR361893
  4. GELFAND, I.- VILENKIN, H., Functii generalizate-Aplicatii ale analizei armonice, Editura Stiintifica si Enciclopedica (Romanian trans.), Bucuresti, 1985. 
  5. GOHBERG, I.- GOLDBERG, S., Basic Operator Theory, 1981, Birkhausen. Zbl0458.47001MR632943
  6. MEGAN, M.- PREDA, P., Conditions for exponential stability of difference equations in Banach spaces, Analele Univ. din Timişoara, vol. xxviii, fasc. 1 (1990), 67-73. Zbl0794.93069MR1140525
  7. MOROZAN, T., Stability and Control for Linear Discrete-time systems with Markov Perturbations, Rev. Roumaine Math. Pures Appl., 40, 5-6 (1995), 471-494. Zbl0862.93068MR1404630
  8. PIETSCH, A., Nuclear Locally Convex Spaces, Springer Verlag, 1972. Zbl0236.46001MR350360
  9. ZABCZYK, J., On Optimal Stochastic Control of Discrete-Time Systems in Hilbert Space, SIAM J. Control, vol. 13, 6 (1974), 1217-1234. Zbl0313.93067MR384291
  10. ZABCZYK, J., Stochastic Control of Discrete-Time Systems, Control Theory and Topics in Funct. Analysis, IAEA, Vienna (1976). Zbl0351.93027MR529600

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