On the leader-following exponential consensus of discrete-time linear multi-agent systems over jointly connected switching networks

The leader-following asymptotic consensus problem for general discrete-time linear multi-agent systems over jointly connected switching networks was solved about a decade ago. Recently, the leader-following exponential consensus was further established using the so-called Krasovskii–LaSalle theorem for a class of discrete-time linear switched systems. But this method involves some advanced concepts such as the weak zero-state detectability of some limiting system. In this paper, we offer a simpler solution to the leader-following exponential consensus problem for general discrete-time linear multi-agent systems over jointly connected switching networks. After converting the solvability of the problem to the establishment of the exponential stability for a class of discrete-time linear switched systems, we first show that this class of linear switched systems is uniformly completely observable. Then, we further conclude that the uniform complete observability for this class of linear switched systems implies the exponential stability for the same class of linear switched systems, thus leading to the solution of the leader-following exponential consensus problem. Moreover, our approach also gives rise to an explicit characterization of the exponential convergence rate of the leader-following consensus problem.