Stabilization Analysis for Nonlinear Systems Under Coupled Fuzzy Controller: A Non-PDC Approach
研究了使用耦合模糊控制器稳定连续非线性系统的方法，通过非并行分布补偿技术和非二次李雅普诺夫函数，推导出线性矩阵不等式条件，确保系统随机渐近稳定并满足H∞扰动衰减准则。
In this study, we present a coupled fuzzy controller design to stabilize a continuous nonlinear system (NS) with external perturbations that are depicted by the Takagi–Sugeno (T–S) fuzzy systems. First, the coupled fuzzy controller is anticipated by incorporating non-parallel distributed compensation (non-PDC) techniques. Then, the proper non-quadratic Lyapunov functional (non-QLF) is taken into account. By employing the time derivatives of non-QLF, Jensen’s inequality techniques, some stabilization conditions are attained in the formulation of linear matrix inequalities to guarantee that the concerned NS is stochastically asymptotically stable together with the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> perturbation damping criterion. Finally, two simulation results are discussed to validate and illustrate the viability of the methodologies we have outlined.