A Synthesis Theory for Nonlinear Systems with Plant Uncertainty

Abstract

A nonlinear plant with parameter uncertainty is imbedded in a feedback system subjected to a finite set of inputs {x. (t)}. For each i there is a specified set of response tolerances. The synthesis procedure guarantees the response tolerances are satisfied over the range of uncertainty, for a large class of plants. The nonlinear plant is converted into an equivalent linear, time-invariant plant with parameter uncertainty, for which exact design is possible. Schauder’s fixed point theorem proves the equivalence is valid. The technique is applicable to any structure for which the equivalent linear, time-invariant problem is solvable.