Global stability of multi-agent systems with heterogeneous transmission and perception functions

Abstract

In this brief, we consider an extended opinion dynamic framework by including both transmitting and perceiving behaviors in the agents’ interactions: the first represents how the agent transmits his own opinion to the neighbors, while the latter models how personal features of the agent affect the final perception of external opinions. The agents’ interactions are modeled by general piecewise linear functions that can be heterogeneous and not necessarily monotone, thus generalizing the analytical framework usually considered in the literature, in particular, the well-known interval consensus (Fontanet al., 2020). In the considered novel multi-agent scenario, we formulate sufficient operative LMI conditions to assess global network asymptotic stability for either a consensus or a cluster equilibrium, without necessarily requiring strong network connectivity. The proposed approach is validated through illustrative examples.