This paper investigates the Takagi–Sugeno (T–S) fuzzy based sliding-mode control (SMC) design of the discrete-time nonlinear model. By constructing a suitable fuzzy membership functions (FMFs) dependent Lyapunov function, the sufficient conditions are derived such that the resultant discrete-time T-S fuzzy model can achieve strictly $(\mathcal{Q},\mathcal{S},\mathcal{R})-\gamma$ dissipative, where $\mathcal{Q},$ $\mathcal{S}$ and $\mathcal{R}$ are known matrices with compatible dimensions satisfying $\mathcal{Q}\le 0$ and $\mathcal{R}={\mathcal{R}}^T,$ and γ is a positive constant. Then, the desired control gain can be obtained by solving a set of linear matrix inequalities (LMIs). Besides that, a fuzzy SMC is designed to assure reaching condition. A modified fuzzy sliding-mode controller is also constructed to adapt input saturation. Finally, simulation results are presented to demonstrate the applicability and effectiveness of the proposed approaches.

本文研究了基于Takagi-Sugeno（TS）模糊的滑模控制（SMC）设计的离散时间非线性模型。通过构造依赖于Lyapunov的合适的模糊隶属函数（FMFs），推导了充分的条件，使得所得到的离散时间TS模糊模型可以严格实现$（\mathcal{问}，\mathcal{小号}，\mathcal{[R}）-\gamma$ 耗散的 $\mathcal{问}，$ $\mathcal{小号}$ 和 $\mathcal{[R}$ 是相容尺寸满足的已知矩阵 $\mathcal{问}\le 0$ 和 $\mathcal{[R}={\mathcal{[R}}^{Ť}，$和γ是正的常数。然后，可以通过求解一组线性矩阵不等式（LMI）获得所需的控制增益。除此之外，还设计了模糊SMC以确保达到条件。还构造了改进的模糊滑模控制器以适应输入饱和度。最后，仿真结果表明了所提出方法的适用性和有效性。