Nonfragile H ∞ Control for Uncertain Takagi–Sugeno Fuzzy Systems Under Digital Communication Channels and Its Application
针对离散时间不确定非线性系统，研究了数字通信信道下非脆弱H∞控制器设计问题，通过线性矩阵不等式给出充分条件，并用仿真验证了方法的有效性。
This work addresses the nonfragile <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> controller design problem for a class of discrete-time uncertain nonlinear systems. The norm-bounded uncertainty is contained in the nonlinear plant, which is described by the well-known Takagi–Sugeno (T–S) fuzzy model. The controller gain perturbation is also considered. When the input signal is transmitted from the controller to the system through the digital communication channels, it will be quantized by a static quantizer. The main attention is to design the nonfragile <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> state-feedback controller for the closed-loop quantized uncertain T–S fuzzy system. By introducing some auxiliary scalars and the fuzzy basis-dependent Lyapunov function approach, sufficient conditions are established in the form of linear matrix inequalities (LMIs). The construction for the nonfragile <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> controller can be completed by solving these LMIs. In the end, the applicability and effectiveness of the proposed method have been illustrated by two simulation examples.