Mode Controllability and Disturbance Rejection in Consensus Networks

This paper considers a new notion of mode controllability for interconnected systems. A new method based on canceling natural system modes that arise from non-zero initial conditions is proposed. A system of first-order linear differential equations is used to represent an interconnected system where the links are static gains. The paper focuses on the initial conditions of the nodes. The system is said to be mode controllable if every initial condition mode can be canceled, while the system is not mode controllable if there exists at least one initial condition mode that cannot be cancelled. A test of model controllability is developed, which is equivalent to the standard controllability. We test this method by rejecting all natural system modes using the minimum input control. Finally, the paper concludes an illustrative example with simulation results and future work.