中文摘要：

讨论了一类线性正则的广义系统的各种能控性和各种能观性的关系,证明了这种广义线性系统的各种能控性和相应的能观性是等价的。同时证明了这种广义系统的快子系统脉冲能控与其快子系统脉冲能观是等价的。其慢子系统能控与其慢子系统能观是等价的。其快子系统能控与其快子系统能观是等价的。

英文摘要：

The relationship between controllability and observability of a kind of linear descriptor system is studied. The equivalence between all kinds of controllability and respective observability of the system is proved. At the same time, the equivalence between impulse controllability and impulse observability of quick subsystem is proved. The equivalence between controuability and observability of slow subsystem is proved. The equivalence between controllability and observability of quick subsystem is proved.