灰色随机线性时滞系统的渐近稳定性

Asymptotic stability of grey stochastic linear delay systems

首先提出了灰色随机线性时滞系统及其渐近稳定性的概念;然后,利用矩阵理论和随机微分时滞方程解的渐近收敛定理及李雅普诺夫函数,研究了灰色随机线性时滞系统的渐近稳定性,得到了随机渐近稳定的几个充分性条件;最后,通过数值例子说明了所得结果在实际应用中的方便性和有效性.

The concepts for grey stochastic linear delay systems and its asymptotic stability are proposed, and the asymptotic stability of grey stochastic linear delay systems is investigated by applying the theory of matrices and the asymptotic convergence theorem for stochastic differential delay equations and constructing the Lyapunov functions. Several sufficient conditions for stochastic asymptotic stabilities are obtained. Finally, a numerical example shows the convenience and effectiveness of the proposed sufficient conditions.