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Linying Xiang [1] and Jonathan J. H. Zhu [2] and Fei Chen [1] and Guanrong Chen [3]

Academic Editor: Wenwu Yu

, 1, , Department of Automation, , Xiamen University, , Xiamen 361005, , China, , xmu.edu.cn,

, 2, , Department of Media and Communication, , City University of Hong Kong, , Hong Kong, , cityu.edu.hk,

, 3, , Department of Electronic Engineering, , City University of Hong Kong, , Hong Kong, , cityu.edu.hk,

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Introduction

Recent technological advances have stimulated broad interests in the notion of network controllability [1–12], which captures the ability to control aggregated dynamics of a networked system and guide it to a desired state by using limited external inputs [13, 14]. In most real dynamical networks, the nodes might have different dynamics. For example, the generators of a power network have different physical parameters and are certainly different from motors, which together form a heterogenous network with nonidentical node dynamics. Therefore, it is of both theoretical and practical importance to study the controllability of networked systems with nonidentical node dynamics, which can help develop a better understanding of the interplay between the complexity of the overall network topology and the collective dynamics of a networked system.

The controllability problem for a leader-follower multiagent system was proposed by Tanner [1], who formulated it as the classical controllability of a single-input linear system and then derived a necessary and sufficient algebraic condition in terms of the eigenvalues and eigenvectors of a submatrix of the graph’s Laplacian matrix. Ji et al. [2] then gave a sufficient condition for multileader controllability based on the algebraic characteristics of a submatrix of the incidence matrix. Subsequently, Rahmani and Mesbahi [3, 4] discussed an intricate relationship between controllability and graph symmetry with respect to the leader and gave a sufficient condition for uncontrollability. Later, Ji et al. studied the controllability in the multileader setting via equitable partitions [5, 6]. It is worth noting that, in the above works [1–6], the interconnection graph is assumed to be connected. Ji et al. [7] introduced the concept of leader-follower...

                                     

 

       

 

  

 

   

 

   

 

 

 

   

   

   

           

     

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