Abstract: The robust stabilization of a class of nonlinear systems in the frame of LMI is studied especially the case of system stabilization via output feedback. The problem of robust stabilization of a class of nonlinear systems is induced into a problem of bilinear matrix inequality(BMI), and then transferred it to an LMI problem by adding constraint. The case of interconnected systems is also discussed. In addition, the validity of this method is verified by numerical example.

Key words: linear matrix inequalities, nonlinear system, output feedback, interconnected system

摘要： 在LMI的框架内探讨不确定非线性系统的鲁棒镇定问题，考虑了利用输出反馈来镇定一类非线性系统。把这类非线性系统的鲁棒综合问题归纳成一个双线性矩阵不等式(BMI)问题，然后通过增加约束将BMI问题转化为线性矩阵不等式(LMI)问题。还利用类似的方法讨论了关联系统的情形。给出了数值算例，验证了这一方法的有效性。

关键词: 线性矩阵不等式, 非线性系统, 输出反馈, 关联系统