Quadratic Stability Bound of Discrete-Time Uncertain Systems

The stability of linear discrete-time systems subject to possibly time varying uncertainties is analyzed. Based on the earlier results, this paper provides a method of directly computing the uncertainty bound allowed for retaining quadratic stability. The algorithm is formulated 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.