H∞ control analysis and design for nonlinear systems

The μ analysis method is applied to a class of multivariable separable autonomous nonlinear feedback systems using sinusoidal input describing function (SIDF). Some properties of the ^∝-norm and structured singular values (SSVs) are shown to hold for the new quasilinear system. The model uncertainty induced by the SIDF approximation is incorporated in the control design as an input multiplicative perturbation. The condition for the absence of limit cycle is derived. The model is then used to design a bank of H_∞ controllers with a simple switching scheme to select the appropriate controller for any operating range. The simulation results are presented to illustrate the performance of the controller.