H^∞-optimal observer-based controller design for nonlinear multivariable systems

We propose a novel algorithm to synthesize an H^∞-optimal observer-based controller for a nonlinear multivariable system. Based on the parametrization of the observer-based controller, a necessary and sufficient condition to achieve robust stability is developed. Moreover, the Nevanlinna-Pick interpolation theory is employed to test the solvability condition of the robust stabilization problem. Optimal robustness can be achieved via the technique of H^∞-optimization. The exact solution of the model-matching problem induced by the stability criterion is solved by the method of noniterative computation of the H^∞-norm.