Convergence and State Reconstruction of Time-Varying Multi-Agent Systems From Complete Observability Theory

We study continuous-time consensus dynamics for multi-agent systems with undirected switching interaction graphs. We establish a necessary and sufficient condition for exponential asymptotic consensus based on the classical theory of complete observability. The proof is remarkably simple compared to similar results in the literature and the conditions for consensus are mild. This observability-based method can also be applied to the case where negatively weighted edges are present. Additionally, as a by-product of the observability based arguments, we show that the nodes' initial value can be recovered from the signals on the edges up to a shift of the network average.

I. Introduction

DISTRIBUTED consensus algorithms [1]– [4] of multi-agent systems have become the foundation of many distributed solutions to in-network control and estimation [5], [6], signal processing [7], and optimization [8], [9]. Convergence conditions of consensus dynamics often play a key role in the performance of such distributed designs, which are relatively well understood under discrete-time network dynamics when the underlying interaction graph is either time-invariant [2], [3], [14] or time-varying [11], [13].