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This paper considers the problem of robust static output H2 controller design for linear parameter-varying (LPV) systems using parameter-dependent Lyapunov functions. The proposed method uses an iterative algorithm that has monotonic convergence to an optimal solution. The proposed design method is also applied to a previously proposed model-following controller design to overcome its drawbacks. We design several model-following controllers for lateral/directional motions of an experimental aircraft and demonstrate controller performance by experiments.