Integral quadratic constraints for delayed nonlinear and parameter-varying systems

The stability and performance of nonlinear and linear parameter varying (LPV) time delayed systems are analyzed. First, the input/output behavior of the time delay operator is bounded in the frequency domain by integral quadratic constraints (IQCs). A simple geometric interpretation is used to derive new IQCs for both constant and varying delays. Second, the performance of nonlinear and LPV delayed systems is bounded using dissipation inequalities that incorporate IQCs. The nonlinear or LPV part of the system is treated directly in the analysis and not bounded by IQCs. This step makes use of recent results that show, under mild technical conditions, that an IQC has an equivalent representation as a finite-horizon time-domain constraint. A numerical example with a nonlinear delayed system is provided to demonstrate the effectiveness of the method.