Theoretical analysis reveals optimal weighted sensitivity minimization for single-input single-output systems, highlighting techniques to manage nonminimum phase and boundary poles.
This paper deals with the design of feedback controllers which minimize theH∞-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 nonminimum phase is elucidated. Finally, a method is introduced for handling plant poles and zeros on the imaginary axis.
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Francis et al. (1984) studied this question.
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