Stability analysis with Popov multipliers and integral quadratic constraints

It is shown that a general form of Popov multipliers can be used in stability analysis based on integral quadratic constraints (IQC). The Popov multiplier is nonproper and a condition that the nominal plant is strictly proper will be imposed in order to ensure boundedness of the IQC corresponding to the Popov multiplier. A consequence of our main result is that the classical Popov criterion can be combined with a stability criterion for slope restricted nonlinearities developed by Zames and Falb. An example shows that the combination of these two criteria is useful in applications.