Sufficient conditions on finite-time input-to-state stability of nonlinear impulsive systems: a relaxed Lyapunov function method

Abstract

This article presents sufficient conditions on Finite-Time Input-to-State Stability (FTISS) of nonlinear impulsive systems, which gathers the analysis of Input-to-State stability (ISS) and finite-time convergence rate. By utilising the Finite-Time Stable Function Pair (FTSFP) and Generalised () function, we established an unified FTISS criterion for nonlinear impulsive systems, in which the impulses maybe beneficial to stabilisation or detrimental to stabilisation. Moreover, a relaxed Lyapunov Function (LF) method is used to investigate FTISS. Compared with the traditional LF method, the main advantage is that the constructed LF is permitted to own indefinite-derivative. As a special case of FTISS, a corollary on Finite-Time Stability (FTS) is established, which is applicable to investigate the realisation of FTS for nonlinear system via impulsive control strategy. Finally, the proposed results are supported by two practical numerical examples.