Minimum Input Selection for Structural Controllability

Given a linear system $\dot{x} = Ax$, where $A$ is an $n \times n$ matrix with $m$ nonzero entries, we consider the problem of finding the smallest set of state variables to affect with an input so that the resulting system is structurally controllable. We further assume we are given a set of "forbidden state variables" $F$ which cannot be affected with an input and which we have to avoid in our selection. Our main result is that this problem can be solved deterministically in $O(n+m \sqrt{n})$ operations

A Class of Uncontrollable Diffusively Coupled Multiagent Systems with Multichain Topologies

<p>We construct systematically a class of uncontrollable diffusively coupled multiagent systems with a single leader and multichain topologies. For studying the controllability of diffusively coupled multiagent systems, such identified uncontrollable systems serve as counterexamples that prove the need to modify the existing sufficient condition using graph partitioning characterization. The uncontrollability of the constructed multichain structures can be preserved when the structures are further augmented to get better connected. The paper also provides an algorithm to obtain the minimal leader-invariant relaxed equitable partition for the graph associated with any diffusively coupled multiagent system guided by a single leader.</p>