ON ROBUST NONLINEAR STABILITY OF INTERVAL CONTROL-SYSTEMS

The classical Lur'e problem considers the stability of a fixed linear time-invariant dynamic system perturbed by nonlinear feedback. This framework is a device to account for unstructured perturbations of the fixed linear system. In this paper, we are concerned with the Lur'e problem when the linear system is also subject to parameter perturbations of uncertainties which are not necessarily small. This motivates us to consider a family of interval plants, i.e., plants with transfer function coefficients varying in prescribed ranges. For such families of systems, we first develop auxiliary results on passivity and strict positive realness which are of interest in their own right. These results are then used to solve the robust version of the Lur'e problem. This solution also allows for the constructive calculation of a guaranteed gain margin for the family of systems under consideration.