A review and comparison of guaranteed cost bounds for robust stability and performance analysis

Lyapunov methods have been used to study stability of nonlinear plants. Likewise, these methods can be used to predict a system´s performance under linear plant model uncertainties and can be used to design controllers to compensate for those same plant uncertainties. These guaranteed cost bounds bound the uncertainty by using modified Lyapunov equations to bound the cost. Various guaranteed cost bounds have been developed for continuous time theory. In this paper, we compare eleven bounds for robust performance analysis; absolute value, linear, inverse, implicit small gain, double commutator, bounded real, positive real, shifted bounded real, shifted positive real, Popov, and shifted Popov. We consider several illustrative examples which involve different types of meaningful uncertainties that show significant performance differences between the bounds