Worst-case stability and performance with mixed parametric and dynamic uncertainties
Résumé
This work deals with computing the worst-case stability and the worst-case H∞ performance of linear time-invariant systems subject to mixed real-parametric and complex-dynamic uncertainties in a compact parameter set. Our novel algorithmic approach is tailored to the properties of the nonsmooth worst-case functions associated with stability and performance, and this leads to a fast and reliable optimization method, which finds good lower bounds of μ. We justify our approach theoretically by proving a local convergence certificate. Because computing μ is known to be NP-hard, our technique should be used in tandem with a classical μ upper bound to assess global optimality. Extensive testing indicates that the technique is practically attractive.