一类离散双线性系统可控性研究

Study on the controllability of a class of discrete-time bilinear systems

在工程中,系统离散化前后可控性是否一致是一个重要问题.近来,Elliott就一类双线性系统,首次构造出了一个连续时不可控、但经离散化后可控的二阶反例.鉴于离散化后的系统可控性无法利用已有方法进行判断,本文给出了一个二阶离散双线性系统可控性的充分条件,从而在更一般情形下得到了一类连续时系统不可控,离散化后可控的反例,深化了对双线性系统可控性的认识.进而,本文证明了对于该类系统,当其阶数大于2时,可控性反例不再存在.

Whether the controllability of a continuous system keeps the consistency after discretization is an important issue in engineering.Recently,a two-dimensional counterexample was constructed by Elliott for an uncontrollable bilinear system and showed that its discrete-time counterpart is,however,controllable.In this paper,a sufficient condition for controllability of a class of second order discrete-time bilinear systems is proposed,which extends the result given by Elliott to more general cases and therefore,deepens our understanding of controllability of bilinear systems.Furthermore,it is shown that the controllability counterexample does not exist if the dimension of such systems is greater than two.