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

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

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.

Original languageEnglish
Article number173
JournalActuators
Volume13
Issue number5
DOIs
StatePublished - May 2024

Keywords

  • Lyapunov theory
  • non-linear control system
  • predefined-time stability
  • sliding mode control

Fingerprint

Dive into the research topics of 'Unified Sufficient Conditions for Predefined-Time Stability of Non-Linear Systems and Its Standard Controller Design'. Together they form a unique fingerprint.

Cite this