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基于Lyapunov稳定性理论，导出了具有滞后时变摄动的线性系统二次稳定的一个充分必要条件，通过求解一个具有线性矩阵不等式约束的凸优化问题，得到了保持系统稳定的最大允许摄动界，文中的例子说明了：和现有的方法相比，本文提出的方法具有更小的保守性．
Based on the Lyapunov stability theory, a necessary and sufficient condition for quadratic stability of linear systems with time-dependent perturbations is derived. By solving a convex optimization problem with linear matrix inequality constraints, the maximum permissible perturbation of the system is obtained The example in this paper shows that the proposed method is less conservative than the existing ones.