Delay-dependent Exponential Stability of Linear Stochastic Neutral Systems with General Delays Described by Stieltjes Integrals

In this paper, mean square exponential stability (MSES) and almost sure exponential stability (ASES) for linear stochastic neutral systems (LSNSs) with general delays described by Stieltjes integrals are investigated. The use of the Stieltjes integrals allows the delays in the system under study to be either discrete, distributed, or a mixture of the two. Sufficient conditions for the linear matrix inequalities (LMIs) in the unified form are obtained by applying stochastic version descriptor system approach and Lyapunov-Krasovskii (L-K) functional based approach. Firstly, the condition based on the form of spectral radius is proposed to ensure the stability of the corresponding difference operator described by Stieltjes integrals. Secondly, differently from the existing delay-dependent stability conditions of LSNSs, the proposed condition depends only on the delays of drift part and independent of the delays of diffusion part. Numerical examples show the effectiveness of the proposed approach finally.