Finite-time global uniform tracking via disturbed hybrid impulsive control

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.