In this paper, we first provide a mathematical description and proof for the robust stability of systems with convex polytopic uncertainty through the construction of attractive invariant sets. Then, we present the problem of estimating the convergence time to arbitrarily tight over-approximations of an invariant set, from both a known initial condition and for initial conditions belonging to a convex polytopic set. We then propose various analytical and numerical methods for computing the aforementioned convergence time. Finally, a number of numerical examples, including a flexible link robotic manipulator, are given to illustrate the results.
CITATION STYLE
McCloy, R. J., De Doná, J. A., & Seron, M. M. (2015). On the estimation of convergence times to invariant sets in convex polytopic uncertain systems. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8955, pp. 62–75). Springer Verlag. https://doi.org/10.1007/978-3-319-14803-8_5
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