Stability analysis of T-S fuzzy state-dependent impulsive nonlinear systems via an extended functional-based approach

In this paper, the authors propose an extended functional-based approach and construct two new extended functionals to investigate the stability of T-S fuzzy state-dependent impulsive system (TSFSIS). Firstly, the conversion of a nonlinear system characterized by state-dependent impulsive inputs is accomplished by employing the B-equivalence method, resulting in fixed-time impulsive system (FIS). Following this, a novel extended functional-based approach that relies on bilateral looped functional (BLF) and Lyapunov function is proposed. In contrast to conventional methods, the extended functionals not only alleviate the constraints on positivity of the Lyapunov function but also encompass a greater wealth of information during impulsive events. By combining the extended functional and some inequalities, sufficient conditions are obtained to ensure the asymptotic stability of TSFSIS. The efficacy of these conditions is validated through two numerical examples.