Robustness analysis of control systems with mixed perturbations

Abstract

The paper considers control systems with parametric as well as unstructured uncertainty. Parametric uncertainty is modelled by a transfer function whose numerator and denominator polynomials are independent uncertain polynomials of the form of P (s, q) = l0 (q) + l1 (q)s +... + ln (q)sn where the coefficients depend linearly on q = [q1, q2,..., qq]T and the uncertainty box is Q = {q: qi∊[[ILLEGIBLE]], i = 1, 2,..., q}. The unstructured uncertainty is modelled as H∞ norm bounded perturbations and perturbations consisting of a family of nonlinear sector bounded feedback gains. Using the geometric structure of the value set of P(s, q), some results are presented for determination of the robust small gain theorem, robust performance, strict positive realness and absolute stability problem of control systems with parametric as well as unstructured uncertainty. Numerical examples are given to illustrate application of the proposed methods.