Robust design of nonlinear control systems using small gain conditions

A method is presented to design robust nonlinear static multivalued controllers. The approach is focused on the adaptive, fuzzy, or neural network based control of an uncertain plant. The performance objectives other than stability are addressed by a previous controller design H₀. Then, using small gain conditions applied to a general transformed feedback loop, a parametrization is presented for all the robustly stabilizing controllers. Finally the robust redesign is obtained as the robustly stabilizing controller H₁ that minimizes a certain distance to the previous design H₀. Simulation examples confirm the feasibility and usefulness of the method