Analysis and design of linear multivariable feedback systems in the presence of additive perturbations

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Abstract
The paper introduces the concept of normal approximations to the analysis of uncertain linear multivariable feedback systems, in order to derive a new criterion for the stability of plants subject to additive perturbations. This criterion permits a complete assessment of stability margins in that it provides a measure of tolerance to uncertainty as well as providing a measure of gain/phase margins. The proposed approach leads to a systematic design procedure which minimizes the effects of uncertainty by attaining the condition of normality or which improves the stability margins by robust gain/phase sharing. The results presented in this paper are insensitive to small perturbations on the nominal plant model and provide the means for a consideration of information concerning the structure of uncertainty.