ℋ∞ control of unstable, uncertain systems using Horowitz bounds

A constrained, two step optimization procedure based on ℋ_∞ loop shaping is suggested for highly unstable plants with large parametric uncertainties. With the proposed controller synthesis, optimality is inherited from the ℋ_∞ design, and robustness to uncertainties is guaranteed by use of Horowitz bounds. This implies that specifications can be made for the worst case of the sensitivity, the complementary sensitivity, and the controller sensitivity functions. The method is applied to a Tokamak fusion reactor for two different types of sensors, and in this example, optimization of one plant design parameter and one controller tuning parameter illustrate the procedure. The results are validated by theory for performance limitations of unstable plants, as well as with a manual search over the two dimensional design and tuning parameter space