广义系统正实反馈控制的一种新方法

A New Approach to Positive Real Feedback Control for Descriptor Systems

研究了广义连续系统的扩展严格正实的控制问题。首先,利用与原系统等价的增广系统和矩阵分解,给出了广义系统正则,无脉冲,稳定且扩展严格正实的一个新的充分必要条件。并且此条件是便于Matlab求解的严格线性矩阵不等式形式。其次,基于此定理和线性矩阵不等式的性质,给出了保证闭环系统是正则,无脉冲,稳定且ESPR的控制器设计方法。最后通过2个数值算例说明了所提出方法的有效性和可行性。

The positive real control problem for singular continuous - time systems is considered. Firstly, by using augmented system which is equivalent to and the characters of linear matrix inequalities, a new necessary and sufficient condition for that singular systems are regular, impulse- free, stable and extended strictly positive real is derived. And this theorem can be constructed by strict LMIs which are solved directly by Matlab. Then, by applying this theorem and the characters of linear matrix inequalities, a state feedback controller is designed to guarantee the closed -loop descriptor systems to be regular, impulse -free, stable and extended strictly positive real. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed method.