Maximum Bound of Quadratic Stability for Possibly Fast Time Varying Polytopic Uncertainties

The stability of linear systems subject to possibly fast time varying uncertainties is analyzed. A condition of quadratic stability is cast in a convex optimization problem. A method of directly computing the maximal bound allowed for retaining quadratic stability is formulted in a two level optimization problem. The inner level of the algorithm consists of choosing an extremum among finite number of values. It is proved that although the outer level of the algorithm is a nonconvex optimization problem, no local minimum distinct from the global minimum can exist. Illustrative examples are presented.