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A Lyapunov-Like Characterization of Predefined-Time Stability

Abstract : 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.
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https://hal-uphf.archives-ouvertes.fr/hal-03424010
Contributor : Mylène Delrue Connect in order to contact the contributor
Submitted on : Wednesday, November 10, 2021 - 11:46:06 AM
Last modification on : Thursday, November 11, 2021 - 4:00:04 AM

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Esteban Jiménez-Rodríguez, Aldo-Jonathan Muñoz-Vázquez, Juan Diego Sanchez-Torres, Michael Defoort, Alexander Loukianov. A Lyapunov-Like Characterization of Predefined-Time Stability. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2020, 65 (11), pp.4922-4927. ⟨10.1109/TAC.2020.2967555⟩. ⟨hal-03424010⟩

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