Actuators (May 2024)

Unified Sufficient Conditions for Predefined-Time Stability of Non-Linear Systems and Its Standard Controller Design

  • Bing Xiao,
  • Haichao Zhang,
  • Shijie Zhao,
  • Zhaoyue Chen,
  • Lu Cao

DOI
https://doi.org/10.3390/act13050173
Journal volume & issue
Vol. 13, no. 5
p. 173

Abstract

Read online

This paper presents a unified Lyapunov-based predefined-time stability theorem that includes three sufficient conditions. The standard theoretical analysis method for achieving predefined-time stability of non-linear systems using this theorem is provided within the framework of Lyapunov theory. The developed Lyapunov-based theorem facilitates the establishment of equivalence between the existing Lyapunov theorems concerning predefined-time stability. Furthermore, when the presented sufficient conditions are relaxed, the predefined-time stability conclusion for non-linear systems degenerates into a finite-time one. Consequently, a standard non-singular sliding mode control framework based on the unified Lyapunov-based theorem is developed for a Lagrangian system to ensure its predefined-time stability. Exemplary numerical simulation results are subsequently given, in order to illustrate the convergence behavior of the system states and confirm that the controlled systems are predefined-time stable.

Keywords