This paper proposed the H ∞ state feedback and H ∞ output feedback design methods for unstable plants, which improved the original H ∞ state feedback and H ∞ output feedback. For the H ∞ state feedback design of unstable plants, it presents the complete robustness constraint which is based on solving Riccati equation and Bode integral. For the H ∞ output feedback design of unstable plants, the medium-frequency band should be considered in particular. Besides, this paper presents the method to select weight function or coefficients in the H ∞ design, which employs Bode integral to optimize the H ∞ design. It takes a magnetic levitation system as an example. The simulation results demonstrate that the optimal performance of perturbation suppression is obtained with the design of robustness constraint. The presented method is of benefit to the general H ∞ design.

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Summary This paper investigates the robust H∞ controller design problem for a class of discrete‐time conic‐type nonlinear systems with time delays and uncertainties. We aim to design a time‐delayed feedback control law such that the closed‐loop conic‐type nonlinear system is asymptotically stable and satisfies the given H∞ performance index from the controlled output to the external disturbance. By selecting a proper Lyapunov function, sufficient conditions related to the H∞ stabilization are formulated in the form of linear matrix inequalities. Finally, a simulation example is employed to demonstrate the effectiveness of the proposed methods.