A design procedure for the exact H^∞ siso‐robust performance problem

Presented in this paper is a loop-shaping solution to the H^∞ robust performance problem for a class of SISO systems. The key feature of this work is the explicit incorporation of phase information into the controller synthesis to facilitate loop-shaping over all frequencies. Consequently, a significant reduction in the required controller gain/bandwidth is achieved. It is also shown that the optimal solution, in the sense of controller gain/bandwidth minimization, to the robust performance problem is that which makes μ = 1 over all frequencies. This is different from the usual definition of optimality in the H_∞/μ literature. An example is included for completeness.