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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2014, Volume 20, Number 3, Pages 263–275
(Mi timm1099)
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This article is cited in 2 scientific papers (total in 2 papers)
Barbashin and Krasovskii's asymptotic stability theorem in application to control systems on smooth manifolds
E. L. Tonkovab a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Udmurt State University
Abstract:
We introduce the notion of so-called standard control system, whose phase space is a finite-dimensional smooth manifold satisfying a series of conditions; in particular, it is supposed to be connected and orientable and have a countable atlas. For a given standard control system, we consider a set of time shifts and construct the closure of this set in the topology of uniform convergence on compact sets. In these terms, we study the conditions of uniform local reachability of a given trajectory. The main result is formulated in terms of a modified Lyapunov function. A simple example is considered.
Keywords:
control systems, uniform local controllability, finite-dimensional smooth manifolds, Lyapunov functions.
Citation:
E. L. Tonkov, “Barbashin and Krasovskii's asymptotic stability theorem in application to control systems on smooth manifolds”, Trudy Inst. Mat. i Mekh. UrO RAN, 20, no. 3, 2014, 263–275; Proc. Steklov Inst. Math. (Suppl.), 291, suppl. 1 (2015), 208–221
Linking options:
https://www.mathnet.ru/eng/timm1099 https://www.mathnet.ru/eng/timm/v20/i3/p263
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Abstract page: | 396 | Full-text PDF : | 100 | References: | 74 | First page: | 12 |
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