Design of Non-fragile Tracking Controller Based on LMI

A tracking controller construction method based on linear matrix inequalities (LMIs) is designed for linear system. The output variables of the reference model are tracked by the output variables of the controlled system via the tracking controller. Different from the existing research results, this paper assumed that the tracking controller has uncertain perturbation, that is, non-fragile problem, so that the designed tracking controller has the ability to resist internal interference. Stability analysis is carried out by H ∞ control theory and Lyapunov stability theory. Then the solution condition of the tracking controller is obtained in the form of LMIs, which could directly solve the gain parameters of the tracking controller through the LMI toolbox of Matlab software. Finally, a simulation experiment is carried out to verify the feasibility of the proposed method.