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线性切换系统是一类重要的混合动态系统。为了深入分析线性切换系统的能控性 ,寻找系统能控性判定的充要条件 ,首次研究了线性切换系统在非奇异变换下的性质。首先 ,证明线性切换系统的能控性在任意非奇异变换下保持不变。其次 ,基于一个恰当的非奇异变换 ,将状态空间适当分解为两个部分 ,给出了一个能控性的必要性条件的新证明。该证明比之已有证明更加简洁直观。最后 ,通过一个具体例 ,验证了能控性在非奇异变换下确实不变。
Linear switching system is a kind of important hybrid dynamic system. In order to deeply analyze the controllability of linear switching systems and find the necessary and sufficient conditions for the system controllability determination, the properties of linear switching systems under non-singular transformation are studied for the first time. First of all, we prove that the controllability of linear switched systems remains unchanged under any non-singular transformation. Secondly, based on an appropriate non-singular transformation, the state space is decomposed into two parts properly, and a new proof of the necessary condition of controllability is given. This certificate is more concise and more intuitive than the one already proven. Finally, through a concrete example, it is verified that the controllability does not change under non-singular transformation.