On robust stability of interval control systems

The authors develop results on the robust stability of a nonlinear control system containing both parametric as well as unstructured uncertainty. The basic system considered is that of the classical Lur´e problem of nonlinear control theory. A robust version of the Lur´e problem consisting of a family of linear time-invariant systems subjected simultaneously to bounded parameter variations and feedback perturbations from a family of sector-bounded nonlinear gains is presently treated. By using the Kharitonov theorem to develop some extremal results on positive realness of interval transfer functions (i.e. a family of rational transfer functions with bounded independent coefficient perturbations), the authors determine the size of a sector of nonlinear feedback gains for which absolute stability can be guaranteed. These calculations amount to the determination of the stability margin of the system under joint parametric and nonlinear feedback perturbations