A mixed IQC approach to nonlinear delay-dependent system analysis

Stability analysis techniques are presented for time-delay systems consisting of the feedback interconnection of a linear time-delay system, with a bounded and casual operator, featuring the nonlinearities, uncertainties, and/or time-varying components of the system. The delays considered are time-invariant but uncertain, residing within a bounded interval including zero. The theorem of integral quadratic constraints (IQC theorem) is employed in a novel fashion to formulate a stability criterion. In this method, the delay elements are replaced by parameter-dependent filters satisfying certain properties, while the nonlinearities are captured by IQCs. It is shown that satisfaction of the IQC analysis condition by the delay-differential system can be guaranteed by satisfaction of it by a finite-dimensional, parameter-dependent system. The KYP lemma is then applied to the latter to obtain a parameter-dependent LMI criterion.