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Finite-time global uniform tracking via disturbed hybrid impulsive control

Author

Listed:
  • Shi, Ya-Dan
  • Jiang, Ming-Han
  • Liu, Bin
  • Zhou, Xiao-Qi

Abstract

This paper investigates the finite-time global uniform tracking (FT-GUT) via disturbed hybrid impulsive control (D-HIC). D-HIC is a type of hybrid impulsive control which is subject to uncertain disturbances. The FT-GUT of the target is equivalent to the finite-time global uniform stability of the error system between the target and the state of tracking system. By using the method of Lyapunov-like functions and the recent GKL-stability of impulsive systems, the criteria for finite-time global uniform stability and the settling time estimates are established. The results are then used to design specific time-triggered and event-triggered D-HIC schemes for affine-type tracking systems to achieve FT-GUT. Both the theoretical results and the numerical simulations show that FT-GUT of the target can be achieved via the designed D-HIC. The main achievements include: less restrictive finite-time global uniform stability conditions are established for impulsive systems; the components from global uniform stability to finite-time global uniform stability are designed into D-HIC, so that the FT-GUT (not just global uniform stability) can be achieved; time-triggered and event-triggered D-HIC are designed for affine-type tracking systems to implement FT-GUT; the time-triggered D-HIC can achieve faster FT-GUT than the event-triggered D-HIC, while the latter has lower impulse frequency; and all D-HICs are anti-disturbance and can eliminate the impact of interference on stability.

Suggested Citation

  • Shi, Ya-Dan & Jiang, Ming-Han & Liu, Bin & Zhou, Xiao-Qi, 2026. "Finite-time global uniform tracking via disturbed hybrid impulsive control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 241(PA), pages 202-219.
    • Handle: RePEc:eee:matcom:v:241:y:2026:i:pa:p:202-219
    DOI: 10.1016/j.matcom.2025.08.012
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    References listed on IDEAS

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    1. Jia Xu & Jitao Sun, 2013. "Finite-time stability of nonlinear switched impulsive systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(5), pages 889-895.
    2. He, Xinyi & Li, Xiaodi & Nieto, Juan J., 2021. "Finite-time stability and stabilization for time-varying systems," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    3. Wu-Hua Chen & Dan-Xia Li & Xiaomei Lu, 2013. "Impulsive observers with variable update intervals for Lipschitz nonlinear time-delay systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(10), pages 1934-1947.
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