Abstract | ||
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This article studies Lyapunov-like conditions to ensure a class of dynamical systems to exhibit predefined-time stability. The origin of a dynamical system is predefined-time stable if it is fixed-time stable, and an upper bound of the settling-time function can be arbitrarily chosen a priori through a suitable selection of the system parameters. We show that the studied Lyapunov-like conditions allow us to demonstrate the equivalence between previous Lyapunov theorems for predefined-time stability for autonomous systems. Moreover, the obtained Lyapunov-like theorem is extended for analyzing the property of predefined-time ultimate boundedness with predefined bound, which is useful when analyzing uncertain dynamical systems. Therefore, the proposed results constitute a general framework for analyzing the predefined-time stability, and they also unify a broad class of systems that present the predefined-time stability property. On the other hand, the proposed framework is used to design robust controllers for affine control systems, which induce predefined-time stability (predefined-time ultimate boundedness of the solutions) w.r.t. to some desired manifold. A simulation example is presented to show the behavior of a developed controller, especially regarding the settling time estimation. |
Year | DOI | Venue |
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2020 | 10.1109/TAC.2020.2967555 | IEEE Transactions on Automatic Control |
Keywords | DocType | Volume |
Nonlinear control systems,predefined-time stability,sliding mode (SM) control,stability of nonlinear systems | Journal | 65 |
Issue | ISSN | Citations |
11 | 0018-9286 | 11 |
PageRank | References | Authors |
0.56 | 6 | 5 |
Name | Order | Citations | PageRank |
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Esteban Jiménez-Rodríguez | 1 | 11 | 0.56 |
A.-J. Munoz-Vazquez | 2 | 42 | 9.97 |
Juan Diego Sanchez-Torres | 3 | 53 | 13.70 |
Michael Defoort | 4 | 433 | 33.97 |
Loukianov, Alexander G. | 5 | 30 | 10.04 |