On the least upper bound for the settling time of a class of fixed-time stable systems
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Fecha
2018-09
Autores
Aldana-López, Rodrigo
Gómez-Gutiérrez, David
Jiménez-Rodríguez, Esteban
Defoort, Michael
Sánchez-Torres, Juan D.
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Descripción
This paper deals with the convergence time analysis of a class of fixed-time stable systems with the aim to provide a new non-conservative upper bound for its settling time. Our contribution is threefold. First, we revisit a well-known class of fixed-time stable systems showing the conservatism of the classical upper estimate of the settling time. Second, we provide the smallest constant that uniformly upper bounds the settling time of any trajectory of the system under consideration. Then, introducing a slight modification of the previous class of fixed-time systems, we propose a new predefined-time convergent algorithm where the least upper bound of the settling time is set a priori as a parameter of the system. This calculation is a valuable contribution toward online differentiators, observers, and controllers in applications with real-time constraints.
Palabras clave
Sliding mode control, Lyapunov stability, Nonlinear systems
Citación
Aldana-López, R., Gómez-Gutiérrez, D., Jiménez-Rodríguez, E., Sánchez-Torres, J.D., & Defoort, M (2018). On the least upper bound for the settling time of a class of fixed-time stable systems. En revisión en: International Journal of Robust and Nonlinear Control.