Mean Square Exponential Stability of Stochastic Stieltjes Integral Delay Systems

In this paper, the mean square exponential stability of a class of stochastic Stieltjes integral delay systems (SSIDSs) is studied. The basic properties and Lyapunov-Krasovskii (L-K) stability theorem with Stieltjes integrals of SSIDSs are discussed firstly. With the help of this theorem, a L-K functional with Stieltjes integrals is introduced to obtain a sufficient stability condition based on linear matrix inequalities (LMIs) by using multiple Jensen inequalities and the nature of stochastic integrals. The use of Stieltjes integrals allows to consider both discrete and distributed delays in the investigated equation. Finally, a numerical example is used to illustrate the effectiveness of the proposed methods.