Consensus of multi-agent systems with faults and mismatches under switched topologies using a delta operator method

Abstract

© 2018 Elsevier B.V. This paper studies the consensus of multi-agent systems with faults and mismatches under switched topologies using a delta operator method. Since faults and mismatches can result in failure of the consensus even for a fixed topology with a spanning tree, how to reach a consensus is a complicated and challenging problem under such circumstances especially when part topologies have no spanning tree. Although some works studied the influence of faults and mismatches on the consensus, there is little work on reaching a consensus for the multi-agent systems with faults and mismatches. In this paper, we introduce the delta operator to unify the consensus analysis for continuous, discrete, or sampled systems under one framework. We develop the theories on the delta operator systems first and then apply theories of the delta operator systems to the consensus problems. By converting the consensus problems into stability problems, we investigate and prove consensus and the associated conditions for systems 1) without any fault, 2) with a known fault, and 3) with unknown faults, under switching topologies with matching or mismatching coefficients. Numerical examples are provided and validate the effectiveness of the theoretical results