中文摘要：

区别于已有Lie代数方法，Lyapunov方法，微分几何方法及不变空间方法，关于定常系统的研究，提出了一种新的方法。从另外一个角度研究形如正：Ar（t）（t）x（t）＋Br（t）（t）u（t），t∈[t0，T]的时变切换系统，通过先构造基于给定的切换序列的一列能控矩阵及其秩条件来研究原切换系统，给出了能控以及能观的一些充分性与必要性条件。

英文摘要：

Different from the Lie algebra method, the common Lyapunov function method, the differential geometry method and the invariant space method for the study of the time-invariant switched systems, a new method is obtained. The known results are all about the time-invariant system, while the condition about the time-varying case has not been concerned yet. The time-varying switched system as the following form is studied. x = Ar（t）（t）x（t） ＋Br（t）（t）u（t）,t ∈ [t0,T] A series of controllable matrixes based on the switching sequence, and the rank condition of them are presented. Some necessary and sufficient conditions about the controllability and observability are presented.