Characterization of Easily Controllable Plants Based on the Finite Frequency Phase/Gain Property: A Magic Number {the square root of}(4 + 2{the square root of}2) in H{sub}∞ Loop Shaping Design

摘要

This paper introduces a phase/gain condition for (marginally) stable systems for characterization of easily controllable systems, and investigates the relationship between the condition and the optimal performance γ{sub}(opt) in H{sub}∞ loop shaping design. More specifically it is shown that there is a close relationship between the condition and a magic number {the square root of}(4 + 2{the square root of}2), for both continuous-time and discrete-time systems. Furthermore a simple design procedure for robust control based on the obtained knowledge is proposed.