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On Finite/Fixed-Time Stability Theorems of Discontinuous Differential Equations

Author

Listed:
  • Luke Li

    (School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China)

  • Dongshu Wang

    (School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China)

Abstract

We investigated the finite/fixed-time stability (FNTS/FXTS) of discontinuous differential equations (DDEs) in this paper. To cope with differential equations that were discontinuous on the right-hand side, we utilized the Filippov solution, which is widely used in engineering. Under the framework of the Filippov solution, we transformed this issue into an FNTS/FXTS problem in the corresponding functional differential inclusion. We proposed some new FNTS/FXTS criteria, which will have important applications in the field of control engineering. It is worth mentioning that the coefficient function in the inequality satisfied by the Lyapunov function (LF) could be indefinite. Moreover, our paper gave a new estimation for the settling time (ST). Finally, two illustrative examples were given to demonstrate the validity and feasibility of the proposed criteria.

Suggested Citation

  • Luke Li & Dongshu Wang, 2022. "On Finite/Fixed-Time Stability Theorems of Discontinuous Differential Equations," Mathematics, MDPI, vol. 10(13), pages 1-14, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2221-:d:847344
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    References listed on IDEAS

    as
    1. Zongyu Zuo & Lin Tie, 2016. "Distributed robust finite-time nonlinear consensus protocols for multi-agent systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(6), pages 1366-1375, April.
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