Abstract: For the Continuous Stirred?Tank （CSTR） with strong?nonlinear, time-varying, pure lag?and other?complex reaction process, a?nonlinear robust?model BMI control?method is proposed. According to the CSTR?mechanism, based on the theoretical analysis?of Lyapunov stability, Lyapunov?function difference?is turned into a?Bilinear Matrix Inequality?（BMI）. By introducing appropriate slack matrix, this method designs a?new?algorithm?for determining the robust stability of? the system, obtains a state feedback controller corresponding to?the closed-loop?system?, leading to  improve generality of the algorithm and performance of the system. Through the simulation experiment?of continuous stirred tank, correctness and effectiveness of the proposed?algorithm are illustrated.

Key words: slack?matrix;?time delay, continuous stirred?tank;?bilinear?matrix inequalities

摘要： 针对具有强非线性、时变、有纯滞后等综合复杂性的连续搅拌釜（CSTR）反应过程，提出了一种非线性鲁棒模型BMI控制方法。该方法根据CSTR的机理，根据Lyapunov稳定性分析理论，将Lyapunov函数差分转化为双线性矩阵不等式（BMI）。该方法引入适当的松弛矩阵，设计出了系统鲁棒稳定性判定的一个新算法，获得了相应闭环系统的状态反馈控制器，提高了算法的通用性，改善系统的性能。通过连续搅拌釜的仿真实验，说明了所提算法的正确性和有效性。

关键词: 松弛矩阵, 时滞, 连续搅拌釜, 双线性矩阵不等式