On optimal sensitivity theory for SISO feedback systems

This paper deals with the design of feedback controllers which minimize the H??-norm of the sensitivity function, suitably weighted. This approach to the theory of feedback design was introduced by Zames [1] and developed by Zames and Francis [2]. In this paper the theory of Sarason [3] is applied to the determination of the optimal weighted sensitivity function and an upper bound on its norm. The problem of achieving small sensitivity over a specified frequency band is studied, and the effect of non-minimum phase is elucidated. Finally, a method is introduced for handling plant poles and zeros on the imaginary axis.