Computing the structured distance to instability
Pierre Apkarian, Dominikus Noll, Laleh Ravanbod · Society for Industrial and Applied Mathematics eBooks · 2015
We analyze robust stability and performance of dynamical systems with real uncertain parameters. We compute criteria like the distance to instability, the worst-case spectral abscissa, or the worst-case H∞-norm, which quantify the degree of robustness of such a system when parameters vary in a given set Δ. As computing these indices is NP-hard, we present a heuristic which finds good lower bounds fast and reliably. Posterior certification is then obtained by an intelligent global strategy. A test bench of 87 systems with up to 70 states 39 uncertain parameters with up to 11 repetitions demonstrates the potential of our approach.