CAJ | 학술논문

分析了在路形拓扑结构下复杂网络的可控性问题。把系统的邻接矩阵进行适当分解，找到邻接矩阵的各子矩阵之间在特征值和特征向量上的关系，进而基于PBH（ Popov－Belevitch－Hautus）判据，得到了复杂网络在路形拓扑结构下系统可控的充要条件。特别地，当控制节点为任意的某一个或多个节点时，给出了路图可控的判别方法。此外，文中提出了不可控特征值的概念，并给出了相应特征值的具体表达形式。文中2个主要定理通过算例进行验证，算例结果与定理结论一致。
분석료재로형탁복결구하복잡망락적가공성문제。파계통적린접구진진행괄당분해，조도린접구진적각자구진지간재특정치화특정향량상적관계，진이기우PBH（ Popov－Belevitch－Hautus）판거，득도료복잡망락재로형탁복결구하계통가공적충요조건。특별지，당공제절점위임의적모일개혹다개절점시，급출료로도가공적판별방법。차외，문중제출료불가공특정치적개념，병급출료상응특정치적구체표체형식。문중2개주요정리통과산례진행험증，산례결과여정리결론일치。
The controllability of complex networks is analyzed in the paper for path topology.With adjacency matrix of the system being decomposed into submatrices, the relationship between eigenvalues and eigenvectors is revealed for the partitioned submatrices.Furthermore, necessary and sufficient conditions are derived by taking advantage of the PBH( Popov-Belevitch-Hautus) criteria.In particular, a method is proposed to determine path controllability when the controlled nodes are any single or multiple nodes, as well as the concept of uncontrollable eigenvalues is presented.The expressions for uncontrollable eigenvalues are provided as well.Two theorems in this paper is veri-fied by examples and the results of examples are in agreement with the conclusion of the theorems.