Control of Heterogeneous Groups of Systems Interconnected Through Directed and Switching Topologies
This note presents a technique to synthesize distributed controllers for the control of heterogeneous systems interconnected through switching directed interaction topologies. Groups of subsystems are defined with undirected interaction within, but directed interconnections between each other. This allows to construct a virtual symmetric interconnection matrix representation of the graph topology. The symmetry guarantees the existence of a diagonalizing transformation, which renders both analysis and synthesis problems particularly simple. Structural constraints on multipliers are used to reduce the complexity of the resulting coupled matrix inequalities to be of the order of a single subsystem times the number of groups. The problem can then be essentially solved by linear fractional transformation (LFT)-based linear parameter-varying (LPV) gain-scheduling synthesis methods, in which the possibly time-varying eigenvalues of the interconnection matrix act as the scheduling variables of the transformed problem.