A Novel Step-Function Method for Stability Analysis of T–S Fuzzy Impulsive Systems

A new stability analysis framework, step-function method, is developed to study the stability of more general impulsive systems, which greatly expands the existing Lyapunov-like stability approaches. The proposed method does not require the monotonicity and continuity of Lyapunov-like functions in each impulsive interval and is expected to address the stability problem for a wider class of hybrid systems, including the state-dependent and event-triggered impulsive systems where the minimal dwell time may vanish. Moreover, the proposed method can also be applied to the stability problem of Zeno point. We propose the construction of one-span step functions and multiple-spans step functions, and present several less-conservative stability conditions for T–S fuzzy impulsive systems. Two examples demonstrate the efficiency of the proposed methods.