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The Barabanov Norm is Generically Unique, Simple, and Easily Computedстатья
Статья опубликована в высокорейтинговом журнале
Статья опубликована в журнале из списка Web of Science и/или Scopus- Автор: Protasov V.Yu
- Журнал: SIAM Journal on Control and Optimization
- Том: 60
- Номер: 4
- Год издания: 2022
- Издательство: Society for Industrial and Applied Mathematics
- Местоположение издательства: United States
- Номер статьи: 21M1426821
- DOI: 10.1137/21M1426821
- Аннотация: We analyze the maximal growth of trajectories of discrete-time linear switching system, i.e., controlled linear systems with the control set being an arbitrary compact set of matrices. This is done by applying the optimal convex Lyapunov function called the Barabanov norm, which provides a very refined analysis of trajectories. Until recently that notion remained rather theoretical apart from special cases. In 2015 N. Guglielmi and M. Zennaro [SIAM J. Matrix Anal. Appl., 36 (2015), pp. 634--655] showed that many systems possess at least one efficiently computed Barabanov norm. In this paper we classify all possible Barabanov norms and prove that, under mild assumptions, which can be verified algorithmically, those norms are unique and are either piecewise-linear or piecewise-quadratic. For some narrow classes of systems, there are more complicated Barabanov norms, but they can still be classified and constructed. Using those results we find all trajectories of the fastest growth. Examples and numerical results are provided.
- Добавил в систему: Протасов Владимир Юрьевич