This paper aims to design a robust observer-based dissipative controller for discrete-time Takagi–Sugeno (T-S) fuzzy systems with nonhomogeneous Markov jumps through a non-parallel distributed compensation (non-PDC) scheme. Based on a mode-dependent nonquadratic Lyapunov function, the final form of the stabilization conditions is expressed as linear matrix inequalities in a less conservative manner. To be specific, this paper proposes a decoupling technique that can address the inherent nonconvex terms by extracting them from the stabilization conditions, where all slack variables are set to be fuzzy-basis-dependent for less conservative performance. Furthermore, the proposed stabilization method adopts a one-step design strategy that simultaneously designs the fuzzy observer and control gains without any iteration procedures by employing a positive tuning parameter. In particular, the time-varying transition probabilities included in the stabilization conditions are effectively removed using a modified relaxation technique that can avoid excessive use of free weighting matrices. Finally, based on four examples, the validity of the proposed method is verified through comparison with other studies.

本文旨在通过非平行分布补偿（non-PDC）方案为具有非齐次马尔可夫跳跃的离散时间Takagi-Sugeno（TS）模糊系统设计一种基于观测器的鲁棒耗散控制器。基于模式相关的非二次 Lyapunov 函数，稳定条件的最终形式以不太保守的方式表示为线性矩阵不等式。具体来说，本文提出了一种解耦技术，该技术可以通过从稳定条件中提取固有的非凸项来解决它们，其中所有松弛变量都设置为与模糊基础相关的，以减少保守的性能。此外，所提出的稳定方法采用一步设计策略，通过采用正调整参数同时设计模糊观测器和控制增益，无需任何迭代程序。特别是，使用改进的松弛技术可以有效地去除稳定条件中包含的时变过渡概率，该技术可以避免过度使用自由加权矩阵。最后，基于四个例子，通过与其他研究的比较，验证了所提方法的有效性。