A Duality‐Based Controllability Condition for a Class of Heterogeneous Networked Systems

In this work, controllability of a class of heterogeneous Networked Control Systems (NCSs) with Multi‐Input Multi‐Output (MIMO), Linear Time Invariant (LTI) nodes is investigated. In general, nodal controllability is not the only factor affecting the controllability of an NCS. We employ the notion of duality to study network controllability and identify a class of NCSs where nodal controllability is the sole deciding factor of network controllability. This identification relies on the equality between the dual of the networked system and the network of duals. We establish that this equality holds for NCSs where all the nodes are actuated and sensed, and the nodal input () and inner‐coupling () matrices coincide at all the nodes (i.e., ). These conditions are inherent in many real‐life systems like networks of spring‐mass systems. An algorithm is designed to check the controllability of networked systems. Numerical implementations of the same in MATLAB indicate the increased time efficiency and consistency as compared with classical controllability algorithms.