Some frequency response methods in feedback control of linear time varying and nonlinear systems

Frequency response methods are very useful in the design of linear, time-invariant systems with parameter uncertainty, such that the system response satisfies specified bounds. These methods are highly transparent permitting the designer to make intelligent trade-offs between sensitivity, complexity of compensation and bandwidth. Schauder´s fixed point theorem permits these same techniques to be used in linear time-varying and nonlinear systems with significant parameter uncertainty. Frequency response methods have also provided precise synthesis techniques for oscillating adaptive systems and for using nonlinear compensation to reduce feedback loop bandwidths.