Control of heterogeneous LPV subsystems interconnected through arbitrary and switching directed topologies

This paper introduces a novel technique for the synthesis of distributed Linear Parameter-Varying (LPV) controllers for heterogeneous LPV systems interconnected through arbitrary, time-varying, directed interaction topologies. A distributed system is constructed from interconnected subsystems for which a novel manipulation of interconnection channels is proposed that renders any interconnection representable as a virtual normal interconnection matrix. This guarantees the existence of a unitary diagonalizing transformation. The synthesis problem can then be essentially solved by Linear Fractional Transformation (LFT)-LPV gain-scheduling synthesis methods, in which the possibly varying eigenvalues of the virtual interconnection matrix act as the scheduling variables of the transformed problem and the computational complexity is in the order of a single subsystem. The method is benchmarked against an existing one and shows superior performance in both a numerical example and the leader-follower formation control problem of LPV quadrocopter models.