A Lyapunov-Like Characterization of Predefined-Time Stability Academic Article uri icon

abstract

  • This technical note 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 to demonstrate 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 predefined-time stability, and they also unify a broad class of systems which 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.

author list (cited authors)

  • Jimnez-Rodrguez, E., Muoz-Vzquez, A. J., Snchez-Torres, J. D., Defoort, M., & Loukianov, A. G.

citation count

  • 8

publication date

  • November 2020