Mixed H2/H∞ multi-channel linear parameter-varying control in discrete time

This paper develops a new method for the synthesis of linear parameter-varying (LPV) controllers in discrete time. LPV plants under consideration have a linear fractional transformation (LFT) representation. In contrast to earlier results which are restricted to single-objective LPV problems, the proposed method can handle a set of H(2)/H(infinity) specifications that can be defined channel-wise. This practically attractive extension is derived by using specific transformations of both the Lyapunov and scaling/multiplier variables in tandem with appropriate linearizing transformations of the controller data and of the controller scheduling function. It is shown that the controller gain-scheduling function can be constructed as an affine matrix-valued function in the polytopic coordinates of the scheduled parameter, hence is easily implemented on line. Finally, these manipulations give rise to a tractable and practical LMI formulation of the multi-objective LPV control problem. (C) 2000 Elsevier Science B.V. All rights reserved.