Nominal H2 Optimization and Simultaneous Stabilization: An Example of U-Parameter Design

The problem considered is that of finding a compensator for a feedback system which minimizes an H²-norm of a weighted sensitivity function for a nominal stable plant while preserving the stability of the feedback system when the nominal plant is perturbed to another, possibly unstable plant. It is known that the problem of simultaneous stabilization of two plants can be reduced to an interpolation problem with units in H^¿. The interpolating unit may be parameterized in terms of an arbitrary strongly bounded real function U(s). This parameterization of robustly stable compensators in terms of bounded real functions is referred to as U-parameterization, and represents a direct extension of the Q-parameter theory used for the design of nominally stable feedback systems. We propose here the use of this free parameter to minimize H²-norm for a nominal plant.