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This paper considers two aspects of the nonlinear H∞ control problem: the use of weighting functions for performance and robustness improvement, as in the linear case, and the development of a successive Galerkin approximation method for the solution of the Hamilton—Jacobi—Isaacs equation that arises in the output-feedback case. Design of nonlinear H∞ controllers obtained by the well-established Taylor approximation and by the proposed Galerkin approximation method applied to a magnetic levitation system are presented for comparison purposes.

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Although the formulation of the nonlinear theory of H ∞ control has been well developed, solving the Hamilton-Jacobi-Isaacs equation remains a challenge and is the major bottleneck for practical application of the theory. Several numerical methods have been proposed for its solution. In this paper, results on convergence and stability for a successive Galerkin approximation approach for nonlinear H ∞ control via output feedback are presented. An example is presented illustrating the application of the algorithm.

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