Synchronization in Networks of Linear Time-Invariant Systems

This thesis studies the synchronization problem for a network of identical, linear time-invariant systems. A criterion to test network synchronization is derived and used for synchronization design. Minimum requirements for the solvability of the design problem are provided. A selection of control protocols for specific classes of systems are presented, and their synchronization properties are characterized. An algorithm to approximate the root locus of polynomials is developed to study synchronization properties in the high-gain limit. This analysis yields an algebraic characterization of systems that synchronize with respect to a large set of interconnections, as well as the conclusion that certain control protocols have poor synchronization properties.M.A.S