Robust controller design based on generalized Bode envelopes

We propose simple tools for robust design of controllers for SISO linear systems with or without uncertainty. These tools are based on the generalization of frequency domain, where the uncertainty is defined by generalized Bode envelopes (GBE). The utilization of generalized Nyquist and Mikhailov theorems, which uses the number of GBE crossings with certain predefined horizontal lines, to deduce stability, allows to obtain stability as well as performance specifications simultaneously. The same design rules can be applied to continuous as well as discrete time systems. We provide examples to demonstrate our method of controller design for various control systems.