基于分散动态补偿的矩形广义系统的正则化与镇定

Regularization and stabilization of rectangular descriptor systems by decentralized dynamic compensation

采用代数方法研究基于分散动态补偿的矩形广义系统的正则化、无脉冲,以及镇定问题.首先给出了补偿后闭环系统正则与无脉冲的充要条件,进而给出矩形广义系统能通过分散动态补偿镇定的充要条件.这些条件涉及一系列简单不等式与等式是否存在正整数解问题.所得结果揭示矩形系统及其动态补偿器的许多新的性质,而且进一步说明对应方形系统与方形或矩形补偿器的结果仍是矩形系统结果的特例.因而,本文结果可以认为是方形系统相应结果的自然推广.另外,给出几个数字例子说明所得结果.

An algebraic approach is proposed to study the problems of regularization, impulse-elimination and stabilization of rectangular descriptor systems by decentralized dynamic compensation. A necessary and sufficient condition for making the closed-loop system both regular and impulse-free is given first. Then, a necessary and sufficient condition to stabilize the closed-loop system by decentralized dynamic compensation is presented. The conditions involve a series of simple inequalities and equalities with solutions of positive integers, and the proposed results reveal some new properties of rectangular systems and their dynamic compensators. It further demonstrates that the results on square systems and square or rectangular compensators are the special cases of the corresponding ones on rectangular systems. Hence these results are natural generalization for that of square systems. Finally, some numerical examples are given to illustrate the results.