Abstract
We discuss a branch and bound algorithm for global optimization of NP-hard problems related to robust stability. This includes computing the distance to instability of a system with uncertain parameters, computing the minimum stability degree of a system over a given set of uncertain parameters, and computing the worst case \(H_\infty \) norm over a given parameter range. The success of our method hinges (1) on the use of an efficient local optimization technique to compute lower bounds fast and reliably, (2) a method with reduced conservatism to compute upper bounds, and (3) the way these elements are favorably combined in the algorithm.
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Ravanbod, L., Noll, D. & Apkarian, P. Branch and bound algorithm with applications to robust stability. J Glob Optim 67, 553–579 (2017). https://doi.org/10.1007/s10898-016-0424-6
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DOI: https://doi.org/10.1007/s10898-016-0424-6