Direct computation of stability bound for systems with polytopic uncertainties

The stability of linear systems subject to possibly fast time-varying uncertainties is analyzed. A method is developed to compute the upper bound of uncertainty size allowed for retaining quadratic stability. The algorithm consists of choosing an extremum among a 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. An illustrative example is presented