A new looped-functional for stability analysis of the linear impulsive system

Abstract A more advanced two-sided looped-functional is adopted for the stability analysis of the linear impulsive system. Compared with existing methods based on functionals relying on Lyapunov’s theorem, the positivity requirement of the functional is relaxed by the looped-functional. The other highlight is the full utilization of information on both the intervals x(tk) to x(t) and x(t) to x ( t k + 1 ) by the two-sided functional. Stability conditions in the form of linear matrix inequality (LMI) derived on the ranged dwell-time are discrete-time stability results, which are expressed in continuous-time. Then, the stability result is further extended to the impulsive system with polytopic uncertainties. Finally, two numerical examples are given to illustrate the effectiveness and advantage of the proposed results.