A Lyapunov-Like Characterization of Predefined-Time Stability

By Esteban Jiménez‐Rodríguez, A. Muñoz‐Vázquez, J. D. Sánchez-Torres, Michael Defoort, Alexander Georgievich Loukianov. IEEE Transactions on Automatic Control, 2019

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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.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/a30273ca0360272415faa757e134a46f047eb25c

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