This paper solves H_∞ controller-based observer synthesis problem for the discrete-time non-linear Markovian jump systems (MJSs) with time-varying delays and disturbances in the existence of partially unknown transition probabilities. The non-linear function considered in this work is assumed to satisfy the one-sided Lipschitz (OSL) condition, which is less conservative as compared to the global Lipschitz condition. Firstly, by virtue of an appropriately chosen Lyapunov-Krasovskii functional and the improved summation inequality, some sufficient inequality-based conditions for the existence of a state feedback controller have been proposed for OSL MJSs such that the overall closed-loop system is stochastically stable (SS). Secondly, an observer-based H_∞ control design problem for the system under consideration has been solved such that the overall error dynamics are SS with disturbance attenuation level γ. The results are formulated in terms of linear matrix inequalities. Finally, a suitable example has been discussed to show the significance of the developed results.

本文解决了ħ _∞为离散时间的非线性马尔可夫跳变系统（MJSs）与部分未知转移概率的存在随时间变化的延迟和干扰基于控制器的观测器的合成的问题。假定在这项工作中考虑的非线性函数满足单侧Lipschitz（OSL）条件，与全局Lipschitz条件相比，该条件不那么保守。首先，借助于适当选择的Lyapunov-Krasovskii泛函和改进的求和不等式的，用于状态反馈控制器的存在一些足够基于不等式条件已被提出用于OSL MJSs使得整个闭环系统是随机稳定（ SS）。其次，基于观察者ħ _∞解决了所考虑系统的控制设计问题，使得总误差动态为具有干扰衰减水平γ的SS 。根据线性矩阵不等式来表示结果。最后，讨论了一个合适的示例以显示所开发结果的重要性。