graph theoretical methods to study controllability and leader selection for dead-time systems

in this article a graph theoretical approach is employed to study some specifications of dynamic systems with time delay in the inputs and states, such as structural controllability and observability. first, the zero and non-zero parameters of a proposed system have been determined, next the general structure of the system is presented by a graph which is constructed by non-zero parameters. the structural controllability and observability of the system is investigated using the corresponding graph. our results are expressed for multi-agents systems with dead-time. as an application we find a minimum set of leaders to control a given multi-agent system.