Synthesis of linear time-varying systems with plant uncertainty by means of integral transforms

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Abstract
This paper deals with the application of integral transforms to the synthesis of linear, time-varying feedback systems with plant uncertainty, in order to achieve specified performance bounds. The condition for a transform to exist over the plant ensemble range is that all plant operators in the ensemble commute with one another. If this condition is satisfied, a transform may be derived suitable for that specific plant ensemble. The detailed design procedure in the transform domain is conceptually identical to that in the Laplace domain for linear time-invariant systems with plant uncertainty, for which exact techniques are available. Quantitative design examples illustrate the design procedure.