### Controllability of General Linear Discrete Multi-Agent Systems with Directed and Weighted Signed Network

ZHAO Lanhao1,2, JI Zhijian1,2, LIU Yungang3, LIN Chong1,2

1. 1. Institute of Complexity Science, College of Automation, Qingdao University, Qingdao 266071, China;
2. Shandong Key Laboratory of Industrial Control Technology, Qingdao University, Qingdao 266071, China;
3. School of Control Science and Engineering, Shandong University, Jinan 250061, China
• Received:2021-02-19 Revised:2021-05-31 Online:2022-11-25 Published:2022-12-23
• Contact: JI Zhijian,Email:jizhijian@pku.edu.cn
• Supported by:
This work was supported by the National Natural Science Foundation of China under Grant Nos. 61873136 and 62033007, Taishan Scholars Climbing Program of Shandong Province of China and Taishan Scholars Project of Shandong Province of China under Grant No. ts20190930.

ZHAO Lanhao, JI Zhijian, LIU Yungang, LIN Chong. Controllability of General Linear Discrete Multi-Agent Systems with Directed and Weighted Signed Network[J]. Journal of Systems Science and Complexity, 2022, 35(6): 2107-2130.

This paper investigates the controllability of general linear discrete-time multi-agent systems with directed and weighted signed networks by using graphic and algebraic methods. The non-delay and delay cases are considered respectively. For the case of no time delay, the upper bound condition of the controllable subspace is given by using the equitable partition method, and the influence of coefficient matrix selection of individual dynamics is illustrated. For the case of single delay and multiple delays, the equitable partition method is extended to deal with time-delay systems, and some conclusions are obtained. In particular, some simplified algebraic criteria for controllability of systems with time delay are obtained by using augmented system method and traditional algebraic controllability criteria.
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