Distributed Algorithm for Controllability Test of Discrete-time Linear Systems

Abstract

This paper investigates the problem to test the controllability of large-scale discrete-time linear systems in a distributed way. The controllability Gramian is the solution of a discrete-time Lyapunov equation. All agents in the large-scale network system solve the discrete-time Lyapunov equation by exchange information with their neighbors. Every agent of the network has access to partial information of the system and has two dynamic estimation variables. A distributed discrete-time algorithm with a constant step size is proposed and a numerical simulation is carried out to verify the convergence property.