Circle and Popov criteria as tools for nonlinear feedback design,

The goal of this paper is to transform classical absolute stability criteria into nonlinear design procedures which employ efficient numerical tools, such as LMI’s. The paper starts with an analysis of an earlier circle criterion design, and shows that its feasibility is limited by conditions on the unstable part of the zero dynamics and on the relative degree. Then, an extended circle criterion design is developed which eliminates the relative degree obstacle. The restrictions on the zero dynamics are relaxed by using the Popov multiplier, which also reduces controller complexity. The results are illustrated on several physically motivated design examples.