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Caputo−Wirtinger integral inequality and its application to stability analysis of fractional-order systems with mixed time-varying delays

Author

Listed:
  • Yang, Xujun
  • Wu, Xiang
  • Song, Qiankun

Abstract

Various techniques of integral inequality are widely used to establish the delay-dependent conditions for the dynamics of differential systems so that the conservatism of conditions can be reduced. In the integer-order systems, the integral term of ∫τωp˙T(s)Sp˙(s)ds often appears in the derivative of Lyapunov−Krasovskii functional, and how to scale down this term to obtain less conservative condition is a key problem. Similarly, the integral term of ∫τω(Dsα0Cp(s))TS0CDsαp(s)ds with fractional derivative may also be encountered in the analysis of dynamical behaviors for fractional-order systems. In view of this, the paper intends to construct several novel fractional Wirtinger integral inequalities under the sense of Caputo derivative, and to investigate the stability of fractional-order systems with mixed time-varying delays based on the constructed Caputo−Wirtinger integral inequalities. Meanwhile, in order to analyze the stability for our concerned models by the new inequalities, two new theorems of generalized fractional-order Lyapunov direct method are given. Finally, a numerical example is designed to validate the correctness and practicability of the obtained results.

Suggested Citation

  • Yang, Xujun & Wu, Xiang & Song, Qiankun, 2024. "Caputo−Wirtinger integral inequality and its application to stability analysis of fractional-order systems with mixed time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 460(C).
    • Handle: RePEc:eee:apmaco:v:460:y:2024:i:c:s0096300323004721
    DOI: 10.1016/j.amc.2023.128303
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