Sampled-Data Control for IT-2 Fuzzy Systems With Packet Losses: Fragmentation-Based Integral Inequality Technique
针对带丢包的二型模糊系统，提出一种基于分段积分不等式的记忆采样数据控制器，将采样区间分为四段，用线性矩阵不等式给出保证系统渐近稳定和H∞性能的充分条件，并在永磁同步电机和弹簧质量模型上验证了有效性。
The focus of this work is on establishing stabilization criteria for interval type-2 (IT-2) fuzzy systems with packet losses using a memory-based sampled-data controller (MBSDC) approach. To accomplish this, first, a new fragmentation-based integral inequality (FBII) is proposed with a more accurate estimation. Additionally, considering a fractional coefficient within the range of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0 < \delta < 1$</tex-math> </inline-formula> , the sampling intervals are divided into four distinct nonuniform segments. These segments encompass the complete sampling details of the intervals: <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$[\xi_{\iota}, \xi_{\iota} + \delta \nu_{1}(\xi))$</tex-math> </inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$[\xi_{\iota} + \delta \nu_{1}(\xi), \xi)$</tex-math> </inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$[\xi, \xi + \delta \nu_{1}(\xi))$</tex-math> </inline-formula> , and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$[\xi + \delta \nu_{1}(\xi), \xi_{\iota+1})$</tex-math> </inline-formula> . Simultaneously, a novel and improved looped-functional is formulated, incorporating both sampling information and transmission delay details. Subsequently, employing the devised FBII technique, specific sufficient conditions are established using linear matrix inequalities (LMIs) to ensure asymptotic stability of the augmented closed-loop systems with respect to 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> -performance index <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\psi$</tex-math> </inline-formula> in the presence of packet losses. Finally, numerical simulations of the Takagi–Sugeno (T–S) fuzzy-based PMSM and mass–spring model are presented, showcasing the effectiveness and superiority of the suggested methodology.