Dynamic Integral Sliding Mode Control of Uncertain Takagi–Sugeno Fuzzy Delayed Systems on Time Scales
研究了时间尺度上不确定Takagi-Sugeno模糊时滞系统的动态积分滑模控制，设计了统一框架下的连续和离散时间控制器，保证全局渐近稳定并避免抖振现象。
This article focuses on dynamic integral sliding mode control (SMC) of uncertain Takagi–Sugeno fuzzy delayed systems on time scales. SMC approaches for both continuous-and discrete-time fuzzy delayed systems are designed in a unified framework. First, we design a dynamic controller to guarantee global asymptotic stabilization (GAS) with <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 the addressed systems. Second, to better adapt to the uncertainty characteristics of fuzzy models, an integral sliding mode surface (SMS) considering states, inputs, and uncertainties is proposed, which is an important contribution of this article. By utilizing the Lyapunov function and timescale calculus, it is shown that all states of the addressed control system can be driven close enough to the SMS and global asymptotic convergence (GAC) of the sliding motion can be ensured under matrix inequality criteria. In addition, the chattering phenomenon near the origin of discrete-time SMC system can be avoided in this article. Finally, three simulation examples are offered to illustrate the feasibility of the proposed control schemes.