A generalized circle criterion and its fields of application

The feedback interconnection of passive systems always leads to a stable control loop. This theorem can be taken as basis for the proof of the circle criterion which allows a stability analysis of closed-loop structures with sector nonlinearities. The circle criterion in its traditional form features an easy graphical evaluation but this advantage must be paid for by conservatism: not all nonlinearities fit sector conditions, and for nonlinearities with more than two inputs a sector evaluation becomes almost unfeasible. With respect to these disadvantages the present paper introduces a less conservative generalized circle criterion and points out its fields of application.