Fractional-Order Vectorial Halanay-Type Inequalities With Applications for Stability and Synchronization Analyses

Peng Liu, Jun Wang, Zhigang Zeng

Research output: Contribution to journalArticlepeer-review

Abstract

The Halanay inequality is widely used in various time-delayed dynamical systems analyses and its vectorial form has become available recently. In this article, the integer-order vectorial Halanay-type inequality is further extended to fractional-order ones in both time-invariant and time-varying forms. It is shown that the fractional-order vectorial Halanay-type inequalities hold under the derived conditions in the form of <inline-formula> <tex-math notation="LaTeX">$M$</tex-math> </inline-formula>-matrices. In addition, the time-invariant inequalities are applied to analyzing the stability and synchronization of fractional-order systems with two numerical examples to substantiate the theoretical results.

Original languageEnglish
Pages (from-to)1-11
Number of pages11
JournalIEEE Transactions on Systems, Man, and Cybernetics: Systems
DOIs
Publication statusAccepted/In press - 2022
Externally publishedYes

Keywords

  • Delay effects
  • Delays
  • Differential equations
  • Fractional-order systems (FoSs)
  • Indexes
  • Numerical stability
  • stability
  • Stability criteria
  • Synchronization
  • synchronization
  • time delay
  • vectorial Halanay-type inequality

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