Robust Synchronization of Uncertain Physically Coupled Heterogeneous Linear Agents

Control of multi-agent systems with physical couplings is motivated by their engineering applications, such as multiple mass-spring-damper systems, power grids, etc., in which each agent not only has information communication but also physical interactions with its neighboring agents. This paper studies robust synchronization problem for uncertain linear agents with physical couplings. We consider the situation where the heterogeneity in agent models is viewed as a memoryless and time-varying parametric uncertainty and where the physical coupling is also considered to be uncertain but norm bounded. Notably, considering these physical couplings to be uncertain makes the robust synchronization problem much more challenging compared to the physically decoupled case. In fact, unlike physically decoupled cases, it is generally difficult to analytically derive synchronization conditions for controller synthesis even if the agents are homogeneous. To this end, we employ a scaled small-gain approach to derive a robust synchronization condition for controller synthesis in terms of linear matrix inequalities.