Regional Consensus for Non-ANCBC Systems with Input Saturation

Abstract

The primary objective of this paper is to study the regional consensus problem for saturated multi-agent systems satisfying solely the stabilization assumption. For such kind of systems, it is recognized that global or semi-global consensus generally cannot be reached. Instead, this paper studies the problem of regional consensus where the initial states of agents lie within a convex set which is positively invariant over a fixed undirected communication network topology. The approach of convex hull representation is extended to deal with the actuator saturation for multi-agents systems. A set of sufficient conditions is derived under which the level set of a quadratic Laplacian function can be used to estimate the domain of consensus. It is shown that these conditions can be transformed into a set of linear matrix inequalities (LMIs), based on which an optimization problem is formulated to obtain the possibly largest estimate of the domain of consensus. A numerical example is presented to illustrate the effectiveness of the proposed method.