An iterative algorithm for maximizing robust performance in H ∞ loop-shaping design

Summary In this paper, an algorithm that gives the best achievable performance bound on a given control problem is proposed using the H∞ loop-shaping design framework. In view of standard design requirements, the robust performance is maximized at low and high frequencies while keeping the robust stability margin above a specified level, and the robust stability margin is directly improved at mid frequencies (around crossover). The proposed frequency-dependent optimization problem is cast in an LMI framework. The resulting solution algorithm simultaneously synthesizes loop-shaping weights and a stabilizing controller that achieve the maximum performance for a given level of robust stability margin corresponding to sufficient gain and phase margins of the closed-loop system. © 2012 John Wiley & Sons, Ltd.