Synthesis of feedback systems with nonlinear time-varying uncertain plants to satisfy quantitative performance specifications

A synthesis procedure for systems with a nonlinear time-varying constrained part (plant) with uncertain parameters, subjected to a finite set of deterministic command and disturbance inputs I = {i^α} is presented. The design must guarantee that in response to i^α, the system output c^α∈ S^α, despite the plant uncertainty, where S^αis a prescribed set of acceptable responses, for that α value. The basic design philosophy is to convert the uncertain nonlinear plant set into an "equivalent" uncertain-linear time-invariant plant set. A synthesis procedure exists for the latter problem. Schauder\´s fixed-point theorem is used to prove that the resulting design satisfies the nonlinear problem. The final design emerges, in general, with linear and nonlinear time-varying compensation networks. Two design examples are included.