Quantitative synthesis of uncertain multiple input-output feedback system

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Abstract
There is given an n input, n output plant with a specified range of parameter uncertainty and specified tolerances on the n2 system response to command functions and the n2 response to disturbance functions. It is shown how Schauder's fixed point theorem may be used to generate a variety of synthesis techniques, for a largo class of such plants. The design guarantees the specifications are satisfied over the range of parameter uncertainty. An attractive property is that design execution is that of successive single-loop designs, with no interaction between them and no iteration necessary. Stability over the range of parameter uncertainty is automatically included. By an additional use of Schauder's theorem, these same synthesis techniques can be rigorously used for quantitative design in the same sense as above, for n × n uncertain non-linear plants, even non-linear time-varying plants, in response to a finite number of inputs.