Low-rank Distributed Consensus Controller Design for Linear Multi-Agent Systems under Randomly Switching Directed Topologies and Model Uncertainties

This paper proposes a novel approach to design distributed consensus controllers for linear MASs subjected to fixed and randomly switching directed topologies and model uncertainties. Employing the idea of selective pole shift based on LQR method, our approach provides a systematic framework to synthesize fully distributed consensus controllers which have low rank and non-conservative coupling strengths. In addition, our approach enables to broaden the class of randomly switching topologies in which the switching component graphs need not to be balanced. Next, we show that all aforementioned remarkable features also apply to the context that dynamics of agents are heterogeneous caused by parametric multiplicative uncertainties in their models. Finally, a numerical example is presented to illustrate the effectiveness of the proposed theoretical approach.