Robust consensus of uncertain linear multi-agent systems via dynamic output feedback

This paper systematically deals with robust consensus of uncertain linear multi-agent systems via dynamic output-feedback protocols. Agents are assumed to have identical nominal linear time-invariant dynamics but are subject to heterogeneous additive stable perturbations. Dynamic output-feedback protocols with or without controller state information exchange between neighboring controllers are studied in a unified framework. Two methods are proposed for protocol design, which need to solve an algebraic Riccati equation and some scalar/matrix inequalities. The first method characterizes some key parameters by scalar inequalities related to the nonzero eigenvalues of the Laplacian, which requires the diagonalizability of the Laplacian, while the second method characterizes the parameters by linear matrix inequalities, which circumvents the requirement of the diagonalizability of the Laplacian. Compared with existing results, the proposed approach can simultaneously cope with heterogeneous uncertainties and directed communication graphs. Numerical results verify the advantages of the proposed design methods.