The optimal projection equations with Petersen-Hollot Bounds: Robust controller synthesis with guaranteed structured stability radius

A feedback control-design problem involving parametric plant uncertainties is considered. A quadratic Lyapunov function suggested by recent work of Petersen and Hollot is utilized for guaranteeing robust stability with robust performance bound for given structured stability radius in the sense of Hinrichsen and Pritchard. Necessary conditions which generalize the optimal projection equations for fixed-order dynamic compensation are used to characterize the controller which minimizes the performance bound. The design equations effectively serve as sufficient conditions for synthesizing controllers possessing robust stability and performance.