Finite-time global uniform tracking via disturbed hybrid impulsive control

Ya-Dan Shi, Ming-Han Jiang, Bin Liu and Xiao-Qi Zhou

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 241, issue PA, 202-219

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.

Keywords: Finite-time stabilization; Finite-time global uniform tracking; Settling time; Impulsive systems; Hybrid impulsive control; Lyapunov-like function (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:241:y:2026:i:pa:p:202-219

DOI: 10.1016/j.matcom.2025.08.012

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