H∞ control based on state observer for vibration isolation platform system

Based on a microvibration isolation platform system dynamic model, the problem of robust H_∞ control for such system is investigated, which contains parametric uncertainties and external disturbances. An H_∞ state-feedback controller based on observers is designed via a Lyapunov approach. The conditions for admissible controllers are formulated in the form of linear matrix inequalities (LMIs), and the controller design is cast into a convex optimization problem subject to LMI and equation constraints. An illustrative example is provided to show the effectiveness of the proposed control design method.