The optimal projection equations with Petersen-Hollot bounds: robust stability and performance via fixed-order dynamic compensation for systems with structured real-valued parameter uncertainty

A feedback control design problem involving structured real-valued plant parameter uncertainties is considered. A quadratic Lyapunov bound suggested by recent work of I.R. Petersen and C.V. Hollot (1986) is utilized in conjunction with the guaranteed cost approach of S.S.L. Chang and T.K.C. Peng (1972) to guarantee robust stability with robust performance bound. Necessary conditions that generalize the optimal projection equations for fixed-order dynamic compensation are used to characterize the controller that minimizes the performance bound. The design equations thus effectively serve as sufficient conditions for synthesizing dynamic output-feedback controllers that provide robust stability and performance