H∞ performance of multi-agent consensus with output feedback and saturated input

Abstract

This article addresses the distributed consensus problem for linear multi-agent systems (MASs) with undirected connected communication topology and saturation limits on the controller input. The networked system has been modeled using a multigraph consisting of directed self-loops. We first represent the saturated control scheme using a polytopic formulation, for appropriate consideration of the control input. Subsequently, we derive sufficient conditions for design of a robust static output feedback controller to achieve consensus of the MAS. The synthesis problem is formulated in the form of linear matrix inequalities for H∞ controller design. Next, the leader-follower topology is considered, with a single leader, for which it is shown that the same controller design technique applies, under a multigraph with single self-loop. Finally, we validate the theoretical results using numerical examples and further simulate the designed control method on a network of spring-mass systems. © 2022 John Wiley & Sons Ltd.