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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 strict and exact control problem of extended continuous systems is studied. First, a new sufficient and necessary condition for the generalized system to be regular, pulse-free, stable and extended strictly strictly is given by using the augmented system equivalent to the original system and the matrix factorization. And this condition is a form of strict linear matrix inequality that is convenient for Matlab to solve. Secondly, based on the theorem and the properties of linear matrix inequalities, a design method of ESPR controller is proposed to ensure that the closed-loop system is regular, pulse-free and stable. Finally, two numerical examples are given to illustrate the effectiveness and feasibility of the proposed method.