Eigenstructure Assignment with Application to Consensus of Linear Heterogeneous Agents

This paper presents a method for designing a feedback controller such that selected outputs of a linear plant exponentially converge to Re-lambda t eta for some scalar eta, with prescribed vector R and non-negative scalar lambda. The controller design is formulated as an eigenstructure assignment problem for which a necessary and sufficient condition for existence of a feasible controller is provided as well as a parameterization of all such controllers. Additionally, the heterogeneous output consensus problem is solved as an eigenstructure assignment problem and a structured controller satisfying communication constraints is provided to achieve consensus of heterogeneous agents. A numerical example demonstrates the efficacy of the eigenstructure method in solving the heterogeneous output consensus problem.