Stability criteria for a class of stochastic distributed delay systems

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Abstract

In the paper linear distributed delay stochastic systems are considered. Using theory of stochastic differential equations sufficient conditions for different kinds of stability are formulated and proved. The article attempts to generalise results presented in the paper [1] and thus theorems proved in [1] become a special case of a generalised approach. The considered class is wider - the function that influence dynamics of a problem can be a real solution of N-degree linear deterministic differential equation. Therefore the generalised reduction technique of distributed delay to lumped delay has to be applied. Criteria for numerous properties of the aforementioned class followed Mao theory designed for point delay systems [2, 3]

[1] B. Ficak, “Point delay methods applied to the investigation of stability for a class of distributed delay systems”, Systems andControl Letters 56, 223-229 (2007).

[2] X. Mao, “Attraction, stability and boundedness for stochastic differential equations”, Nonlinear Anal. 47 (7), 4795-4806 (2001).

[3] X. Mao, (1994), “Exponential stability of stochastic differential equations”, in Monographs and Textbooks in Pure and AppliedMathematics Series, pp. 307, Marcel Dekker, New York, 1994.

[4] B. Ficak, “Application and mathematical properties of time delay diffusion models”, J. Mathematical Finance (2013), (to be published).

[5] M. Buslowicz, “Robust stability of the new general 2D model of a class of continuous-discrete linear systems”, Bull. Pol. Ac.: Tech. 58 (4), 561-565 (2010).

[6] M. Buslowicz, “Robust stability of positive discrete-time linear systems of fractional order”, Bull. Pol. Ac.: Tech. 58 (4), 567-572 (2010).

[7] M. Buslowicz, “Robust stability of positive continuous-time linear systems with delays”, Int. J. Appl. Math. Comput. Sci. 20 (4), 665-670 (2010).

[8] E. Verriest, “Linear systems with rational distributed delay: reduction and stability”, Proc. 1999 Eur. Control Conf. DA-12, CD-ROM (1999).

[9] E. Verriest, “Stochastic stability of a class of distributed delay system”, 44th IEEE Conf. on Decision and Control 1, CDROM (2005).

[10] P. Florchinger, “Lyapunov-like techniques for stochastic stability”, SIAM J. Control and Optimization 33, 1151-1169 (1995).

[11] V.B. Kolmanovskii, V.R. Nosov, Stability of Functional DifferentialEquations, Academic Press, New York, 1986.

[12] X. Mao, Stochastic Differential Delayed Equations, Springer, Berlin, 2003.

[13] X. Mao, Stochastic Differential Equations and Applications, pp. 366, Horwood Publishing, Chichester, 1997.

[14] J. Tancula and J. Klamka, “Examination of robust stability of computer networks”, Proc. 6-th Working Int. Conf. “PerformanceModelling and Evaluation of Heterogenous Networks” 1, CD-ROM (2010).

Bulletin of the Polish Academy of Sciences Technical Sciences

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