Abstract This paper is focused on a novel observer-based sliding mode control strategy for a class of uncertain stochastic Markovian jump systems with nonlinear perturbation. A novel linear switching surface scheme is established for the system with the aid of a simplified non-fragile observer, from which the corresponding reaching motion adaptive control law is synthesized. Then, a new sufficient condition of exponential stability for the associated dynamics during the sliding mode is derived based upon the designed sliding function and linear matrix inequality approach. At last, two illustrative examples are conducted to justify the effectiveness and applicability of the proposed methodology.

中文翻译：

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基于非脆弱观测器的不确定非线性随机马尔可夫跳跃系统的滑模自适应控制

摘要 本文针对一类具有非线性扰动的不确定随机马尔可夫跳跃系统，研究了一种新的基于观测器的滑模控制策略。借助简化的非脆弱观测器为系统建立了一种新颖的线性切换面方案，并从中综合出相应的到达运动自适应控制律。然后，基于设计的滑动函数和线性矩阵不等式方法，推导出滑模期间相关动力学的指数稳定性的新充分条件。最后，进行了两个说明性示例来证明所提出方法的有效性和适用性。