Control of heterogeneous groups of LPV systems interconnected through directed and switching topologies

A technique to synthesize distributed linear parameter-varying (LPV) controllers for the control of heterogeneous LPV systems interconnected through switching directed interaction topologies is presented. 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 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 be solved by modified linear fractional transformation (LFT)-based LPV gain-scheduling synthesis methods.