Stability Analysis of T‐S Fuzzy State‐Dependent Impulsive Nonlinear Systems Based on New Improved Functional

ABSTRACT In this paper, the authors propose an extended functional‐based approach and develop two new improved functionals to investigate the stability of T‐S fuzzy nonlinear systems with state‐dependent impulsive inputs (TSFSSI). Firstly, the conversion of nonlinear systems characterized by state‐dependent impulsive inputs is accomplished by employing the T‐S fuzzy model and B‐equivalence method, resulting in T‐S fuzzy nonlinear systems with fixed‐time impulsive inputs (TSFSFI). Secondly, two novel improved functionals that rely on bilateral looped functional (BLF), Lyapunov functions, and additional new functional elements are proposed. In contrast to BLF, the improved functionals not only alleviate the positivity constraints on Lyapunov functions, thereby reducing the conservativeness of stability conditions, but also impose fewer restrictions on the functional construction. Leveraging these enhanced functionals along with certain inequalities, sufficient conditions are obtained to ensure the asymptotic stability of TSFSSI. Finally, the effectiveness of the proposed conditions is validated through two application examples.