Finite-Time Practical Incremental Stability of Impulsive Systems with Application to Design of Impulsive Control

This paper investigates finite-time practical incremental stability (FTPIS) for impulsive systems with application to the design of impulsive control. The notions of FTPIS and finite-time practical stability (FTPS) are proposed for impulsive systems. By employing the methods of Lyapunov-like function and dwell-time, FTPIS criteria with FTPIS settling time estimates are established for impulsive systems. The results are then used to design FTPIS-based impulsive control, including time-triggered impulsive control (T-IC), time-state-triggered impulsive control (TS-IC), and state-triggered impulsive control (S-IC). To verify the validity of the theoretical results, one example on the problem of finite-time practical tracking is given. Both theoretical results and numerical simulations show that, compared with T-IC and S-IC, TS-IC has advantages, with the shortest settling time, the least number of impulsive control required to reach the settling time, and the lowest impulse frequency. Additionally, the designed TS-IC improves the mechanism of impulsive control in the literature, which is either time-triggered or state-triggered.