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中文摘要：
针对饱和线性系统，借助二次型Lyapunov函数，估计稳定域的一个严格子集。同时为了减少保守性，利用矩阵的Schur补性质，将如何选取该二次型Lyapunov函数的问题转化为标准的LMI凸优化问题。将该方法应用于电力系统，提出一种判断饱和PSS控制是否有效的方法。其主要思路是估计出饱和系统的稳定域，通过分析预想扰动的状态量是否位于估计的稳定域内，从而为判断此饱和PSS控制是否能有效镇定预想的扰动提供判据，利用算例验证了方法的有效性。
英文摘要：
A quadratic Lyapunov function is employed to estimate the stability region of a linear system with saturation nonlinearity. To reduce the conservatism in the estimation, the Schur complements of the matrixes are applied to transform the problem of selecting a suitable quadratic Lyapunov function into a simple convex optimization problem with linear matrix inequality （LMI） constraints. The method of stability region estimation is further applied to power systems with the saturated power system stabilizer （PSS）, and a method is introduced to analyze the performance of the saturated controllers by checking whether the expected initial states of a power system resides inside the estimated stability region or not, Simulation tests demonstrate the approach is effective.
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