This paper mainly discusses ${\mathcal{H}}_{\infty }$ finite-time realization for a class of uncertain Markovian jump systems (MJSs) with unmeasurable state via sliding mode control (SMC) method. A key question is how to design an appropriate SMC approach in a finite-time to reduce the effects of model switching and external interference on the overall performance of the system under consideration. First, by designing an appropriate finite-time SMC law based on a non-fragile observer, the state trajectory can reach a specified sliding surface (SSS) within given finite-time interval. Then, by means of time-partitioning strategy, finite-time boundedness (FTBs) criteria including the reaching phase and the sliding motion phase are proposed for uncertain MJSs with ${\mathcal{H}}_{\infty }$ performance. Second, by solving the corresponding linear matrix inequalities (LMIs), the controller gain and the observer gain are obtained. Finally, a single-link robot arm model (S-LRAM) is given to prove the effectiveness of the proposed method.

本文主要讨论 ${\mathcal{H}}_{\infty }$通过滑模控制（SMC）方法对一类具有不可测量状态的不确定马尔可夫跳跃系统（MJS）进行有限时间实现。一个关键问题是如何在有限时间内设计合适的 SMC 方法，以减少模型切换和外部干扰对所考虑系统整体性能的影响。首先，通过基于非脆弱观察者设计适当的有限时间 SMC 定律，状态轨迹可以在给定的有限时间间隔内到达指定的滑动面 (SSS)。然后，通过时间划分策略，针对不确定的 MJS，提出了包括到达阶段和滑动阶段的有限时间有界（FTB）准则。${\mathcal{H}}_{\infty }$表现。其次，通过求解相应的线性矩阵不等式 (LMI)，获得控制器增益和观测器增益。最后，给出了一个单连杆机械臂模型（S-LRAM）来证明所提出方法的有效性。