Application of Fixed Point Theory to Uncertain Nonlinear and MIMO Feedback Problems

The essence of fixed point theory in feedback design is to replace the difficult parts of the design problem by others involving either uncertain linear time invariant (LTI) elements and/or disturbance sets. Since plant parameter and/or disturbance uncertainty is anyhow the basic problem in feedback design, this eliminates to a large extent the differences between linear and nonlinear systems. If compensators can be found to solve the new equivalent LTI problem, then these same compensators are guaranteed to solve the original much more difficult problem. Three such applications of fixed point theory are presented for generating simple LTI equivalent problems which replace the original nonlinear and MIMO design problems.