New Fixed-Time Stability Theorems for Delayed Fractional-Order Systems and Applications

Udhayakumar Kandasamy, Fathalla A. Rihan, Rakkiyappan Rajan, Mahmoud M. El-Khouly

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


This paper examines the problem of improved fixed-time stability for generalized delayed fractional-order systems (FOSs). As a first step, some stability conditions are presented in two theorems to verify fixed-time stability (F-TS) of FOSs by using Lyapunov stability theory and indefinite Lyapunov functionals, where the fractional-order derivative of the indefinite functions may not exist. Furthermore, the corresponding estimated settling time of FOSs is also provided. Second, the results are extended to study fractional-order neural networks (FONNs) with time-delays in fixed-time synchronization. Using the Dirac delta functions, we propose an explicit saturated impulsive controller to synchronize the master and slave systems. Moreover, by constructing suitable indefinite Lyapunov-Krasovskii functions (LKF), we derive algebraic conditions to guarantee the fixed-time synchronization of the addressed FONNs. The simulation results demonstrate the feasibility and efficacy of the proposed method.

Original languageEnglish
Pages (from-to)63230-63244
Number of pages15
JournalIEEE Access
Publication statusPublished - 2022


  • Fractional-order
  • Lyapunov function
  • fixed-time stability
  • impulsive control
  • indefinite functional
  • saturation
  • time-delay

ASJC Scopus subject areas

  • General Engineering
  • General Computer Science
  • General Materials Science


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