Design of robust pre‐compensators for decoupling polytopic linear systems

Abstract

SummaryThis work proposes a new approach for designing dynamic pre‐compensators to reduce interactions of multivariable uncertain square systems. The proposed method is based on the minimization of the norm of the difference between the compensated system and a diagonal reference model. The main appeal of the technique is to propose a systematic procedure to obtain the reference model dynamics, in contrast to methods that use the identity matrix as a reference, and to obtain diagonal dominance in a frequency range of interest employing the generalized Kalman‐Yakubovich‐Popov (KYP) Lemma. The design conditions are expressed as linear matrix inequalities (LMI) thanks to a new general parametrization on the decision variables in bilinear products to reduce the conservatism of the solutions compared to standard approaches from the literature. Numerical examples verify the robustness of the proposed method, showing significant decoupling of the uncertain plant.