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The complete controllability of multi-agent systems are mainly focused on the whole system referring to transferring the remaining agents of such system from any arbitrary initial state to any final state by controlling dynamics of a small amount of agents under exchanged information between each other, which makes the system reflect the effect of a whole. However, in practice, it may not be necessary to ensure all nodes be controllable. This paper mainly investigates the partial controllability of multi-agent systems under undirected fixed topology. The concept of partial controllability is proposed and some sufficient and necessary conditions are proposed for the partial controllability of continuous-time multi-agent systems with multiple leaders. Numerical example and simulations are presented to illustrate the theoretical results.

This paper focuses on the consensus problem for second-order multi-agent systems with impulsive algorithm and communication time-delays. By introducing a state transformation, the consensus of the system is translated into the asymptotical stability of a reduced-order discrete-time system. Based on the properties of Laplacian matrix of graphs and a given invertible matrix, necessary and sufficient conditions are established for the consensus convergence in the cases of directed and undirected topologies. Two numerical simulations are worked out to illustrate the effectiveness of the theoretical results.