Controllability of networked systems with heterogeneous dynamics

Hao et al. (Int J Robust Nonlinear Control 28(5):1778–1788, 1976) established necessary and sufficient conditions for the controllability of homogeneous networked systems where the individual nodes are linear time-invariant (LTI) systems and the network topology matrix is diagonalizable. In this paper, we consider a class of heterogeneous networked systems having triangularizable network topology. Here, we establish a result which gives necessary and sufficient conditions for controllability of a class of heterogeneous systems, which generalizes the result of Hao et al. (Int J Robust Nonlinear Control 28(5):1778–1788, 1976). Also, we provide some necessary conditions for the controllability of general heterogeneous networked systems having some restrictions on the network topology matrix. Theoretical results are illustrated with numerical examples.