APPLICATIONS OF OPTIMIZATION METHODS TO ROBUST STABILITY OF LINEAR-SYSTEMS

We study the robust stability problem for a family of polynomials. We allow for all the coefficients of the polynomials to be affinely pertu rbed, where the size of the perturbation is measured by an arbitrary c onvex function. We apply optimization techniques, and in particular co nvex duality methods, to derive simple formulas for the stability radi us, to find a minimal perturbation which destroys stability, and to ob tain necessary and sufficient conditions for robust stability. Our fra mework is general enough to cover many applications. As special cases, we obtain many results recently reported in the literature.