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A new vertex result for robustness problems with interval matrix uncertainty. (English) Zbl 1154.93023
Summary: This paper addresses a family of robustness problems in which the system under consideration is affected by interval matrix uncertainty. The main contribution of the paper is a new vertex result that drastically reduces the number of extreme realizations required to check robust feasibility. This vertex result allows one to solve, in a deterministic way and without introducing conservatism, the corresponding robustness problem for small and medium size problems. For example, consider quadratic stability of an autonomous $n_x$ dimensional system. In this case, instead of checking $2^{n_x^2}$ vertices, we show that it suffices to check $2^{2n_x}$ specially constructed systems. This solution is still exponential, but this is not surprising because the problem is NP-hard. Finally, vertex extensions to multiaffine interval families and some sufficient conditions (in LMI form) for robust feasibility are presented. Some illustrative examples are also given.

##### MSC:
 93B35 Sensitivity (robustness) of control systems 93C41 Control problems with incomplete information 93D99 Stability of control systems
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