Finite‐time practical stability of impulsive systems with application to design of impulsive control

Abstract This paper studies the finite‐time practical stability (FTPS) of impulsive systems with application to design of impulsive control. The notions of FTPS and global FTPS are proposed. The criteria of local and global FTPS are established for impulsive systems. And the estimates of settling time for FTPS are obtained. Moreover, the FTPS results are used to design three types of impulsive control, including time‐based impulsive control (T‐IC), state‐based impulsive control (S‐IC), and time‐state‐mixed impulsive control (T‐S‐IC) for FTPS of unstable systems. Two examples are given to verify the theoretical results. The FTPS criteria are shown to relax the requirement on power exponent term of Lyapunov‐like function for FTS. And both theoretical and simulation results show that T‐S‐IC achieves the best performance with the shortest settling time and the least number of impulses compared with the purely time‐based T‐IC and the purely state‐based S‐IC.