基于代数判据的奇异系统输出反馈设计新方法

New Output Feedback Design Method for Singular Systems Based on Algebraic Criteria

针对奇异系统提出一种静态输出反馈控制设计新方法.首先,利用矩阵迹不等式研究奇异系统容许性问题,并提出奇异系统容许(正则、无脉冲、稳定)的代数判据.其次,在系统容许性分析理论结果基础上,设计静态输出反馈控制器保证闭环奇异系统容许性,同时给出矩阵迹不等式的求解方法完成输出反馈控制器设计.与已有的基于线性矩阵不等式求解静态输出反馈控制器方法不同,本文所提方法不需要对输出矩阵进行特殊设定.最后,通过仿真例子表明所提理论方法的可行性和有效性,并且此方法也适用于正常系统输出反馈控制设计.

A new design method of the static output feedback control for singular systems is proposed. Firstly, by using the matrix trace inequality, the admissibility issue of singular systems is introduced and the algebraic criteria of admissibility for this kind of systems is established. Secondly, based on the admissibility analysis result, the sufficient condition for static output feedback controller design is obtained to ensure the admissibility for closed-loop systems. Meanwhile, the solving method of matrix trace inequality is given to obtain the gain matrix. Different from the design method of static output feedback controller via linear matrix inequalities, the proposed method does not need the special requirement setting of output matrix. Finally, three numerical examples illustrate the feasibility and effectiveness of the proposed theoretical method, which also applies for the output feedback controller design of normal systems.