离散区间二型Tagaki-Sugeno模型时滞系统广义耗散控制设计
Extended dissipative control design for discrete-time interval type–2 Tagaki-Sugeno model based systems with time-varying delays

对带有时变时滞和外部扰动的一类离散区间二型 Tagaki-Sugeno(T-S) 模型非线性系统，研究了其广义耗散性能分析与状态反馈控制器的设计问题。与一型T-S模糊系统相比，区间二型模糊系统能更好地处理隶属函数中的不确定信息。首先，通过模型转换的方法，对系统的滞后状态进行变换，从而将时变时滞的不确定性从原系统中分离出。根据转换后的仅含定常时滞和具有有界误差范数的两个子系统，利用时滞依赖的李雅普诺夫-克拉索夫斯基泛函方法推导出了使系统渐近稳定并具有广义耗散性能的充分条件。接着，设计了保证闭环系统渐近稳定并具有广义耗散性能指标的状态反馈控制器。最后由数值仿真验证了设计方法的有效性。
The problems of extended dissipativity analysis and state feedback controller design are investigated for a class of interval type-2 discrete-time Tagaki-Sugeno(T-S) model nonlinear systems with time-varying delays. Compared with type-1 model, the interval type-2 T-S based nonlinear systems can represent and capture the uncertain knowledge and information contained in membership functions. First, by employing model transformation method, the time varying delay uncertainty is pulled out of the original system. So the system underlying can be decomposed into a linear time-invariant subsystem and a norm-bounded uncertain subsystem. A sufficient asymptoic stability condition of the extended dissipativity is established by a delay-dependent Lyapunov-Krasovskii functional. Then a interval type-2 controller is designed to guarantee the asymptoic stability and the extended dissipative performance of the closed-loop system. Finally, the simulation demonstrates the effectiveness of the proposed extended dissipative control method.