Exponential stability of stochastic delay interval systems. (English) Zbl 0949.60068

Liao, X. X.; Mao, X.

Syst. Control Lett. 40, No. 3, 171-181 (2000).

Although deterministic interval systems have received a great deal of attention, so far there is no work on stochastic interval systems. The main aim of this paper is to initiate the study of stochastic interval systems. Of course, there are many properties of such systems to be investigated, but this paper will concentrate on the study of exponential stability of stochastic interval systems with time-varying delays. The main technique used in this paper is the Razumikhin-type theorem established recently by the second author [Stochastic Processes Appl. 65, No. 2, 233-250 (1996; Zbl 0889.60062)].

MSC:

60H10

Stochastic ordinary differential equations (aspects of stochastic analysis)

Keywords:

stochastic interval system; Razumikhin-type theorem; Brownian motion; Itô’s formula

Citations:

Zbl 0889.60062

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