Region Stability/Stabilization and H∞ Control for Discrete-Time Impulsive Takagi-Sugeno Fuzzy Systems

This article focuses on the issues of region stability/stabilization and H-infinity control for discrete-time impulsive Takagi-Sugeno fuzzy systems (DTIT-SFSs). First, a more accurate asymptotic stability criterion is proposed by introducing the definition of region stability. It offers a more precise estimation of convergence speed and damping response for DTIT-SFSs compared with the conventional stability criteria in terms of dynamic performance. Second, a fuzzy controller is designed based on the aforementioned region stability analysis, which can effectively control the convergence rate to the equilibrium state and ensure the desired damping response of DTIT-SFSs. Furthermore, a novel H-infinity fuzzy controller is designed, ensuring both a certain level of H-infinity performance of DTIT-SFSs and constraint on the convergence speed and damping response of DTIT-SFSs. Finally, the functionality of this technique is validated through numerical calculations and an inverted pendulum control example.