Robust stability of the systems with mixed uncertainties under the IQC descriptions

This paper studies the problem of robust stability checking for a single-input single-output uncertain feedback system which consists of a linear uncertain plant in the forward loop and a non-linear dynamic uncertain unit in the feedback loop. It is supposed that the linear part of the system is of parametric uncertainties described by a polytopic perturbation mode, and that the non-linear part of the system is of dynamic uncertainties characterized by an integral quadratic constraint (IQC). The problem of stability checking is discussed for different structures of the IQC multiplier based on the concepts of biconvex and convex-concave functions and their properties. For different uncertainty structures of the system, a finite vertex checking result and an edge checking result are presented. As an application of the above results, the problem of robust H performance checking is discussed for the case that the uncertain plant of a feedback system is parameterized by a polytopic perturbation mode, and an edge checking result is given under a fairly mild assumption. Also, the absolute stability of an interval system is investigated, and the vertex results of circle criterion and Popov criterion are obtained. Finally, a demonstrating example is included.