Region Stability/Stabilization and $H_{\infty }$ Control for Discrete-Time Impulsive Takagi–Sugeno Fuzzy Systems
Tingting Zhang, Huasheng Zhang, Xiangpeng Xie
Abstract
This paper focuses on the issues of region stability/stabilization and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control for discrete-time impulsive Takagi-Sugeno fuzzy systems (DTIT-SFSs). Firstly, 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 to conventional stability criteria in terms of dynamic performance. Secondly, 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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> fuzzy controller is designed, ensuring both a certain level of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> 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