Stabilization of Stochastic Markovian Jump Systems with Partially Unknown Transition Probabilities and Multiplicative Noise

Zhao Yong; Fu You

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Stabilization of Stochastic Markovian Jump Systems with Partially Unknown Transition Probabilities and Multiplicative Noise

机译：具有未知转移概率和可乘噪声的随机马尔可夫跳跃系统的镇定

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We are concerned with the problems of stability and stabilization for stochastic Markovian jump systems subject to partially unknown transition probabilities andmultiplicative noise, including the continuous- and discrete-time cases. Sufficient conditions guaranteeing systems considered to be asymptotically stable in the mean square are presented in the form of LMIs. Furthermore, the desired state feedback controllers are designed. It is shown that, by introducing the free-weighing matrix method, the results we have obtained not only are less conservative than the existing ones but also can be regarded as extensions of the corresponding results of Markovian jump systems without noise. Numerical examples are finally provided to illustrate the effectiveness of the proposed theoretical results.

机译：我们关注随机马尔可夫跳跃系统的稳定性和稳定性问题，该系统具有部分未知的转移概率和乘性噪声，包括连续时间和离散时间情况。 LMI形式提供了足够的条件保证系统被认为在均方渐近稳定。此外，设计了所需的状态反馈控制器。结果表明，通过引入自由加权矩阵法，我们获得的结果不仅不如已有的保守，而且可以看作是无噪声的马尔可夫跳跃系统的相应结果的扩展。最后提供了数值例子来说明所提出的理论结果的有效性。

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《Mathematical Problems in Engineering》 |2017年第9期|6194598.1-6194598.9|共9页
作者
Zhao Yong; Fu You;
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Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Peoples R China;

Shandong Univ Sci & Technol, Coll Comp Sci & Engn, Qingdao 266590, Peoples R China;

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1. Stochastic stability and stabilization of discrete-time singular Markovian jump systems with partially unknown transition probabilities [J] . Wang Jianhua, Zhang Qingling, Yan Xing-Gang, International Journal of Robust and Nonlinear Control . 2015,第10期

机译：转移概率部分未知的离散时间奇异马尔可夫跳跃系统的随机稳定性和稳定性
2. STABILIZATION OF DISCRETE-TIME MARKOVIAN JUMP SYSTEMS WITH PARTIALLY UNKNOWN TRANSITION PROBABILITIES [J] . Qingling Zhang, Guoliang Wang, Wanquan Liu, Discrete and continuous dynamical systems . 2011,第4期

机译：具有未知转移概率的离散马尔可夫跳跃系统的镇定
3. Stochastic Stabilization of Markovian Jump Systems with Partial Unknown Transition Probabilities and Actuator Saturation [J] . Yijing Wang, Zhiqiang Zuo, Yulong Cui Circuits, systems, and signal processing . 2012,第1期

机译：具有未知转移概率和执行器饱和的Markovian跳跃系统的随机镇定
4. Stochastic admissibility for a class of nonlinear singular Markovian jump systems with time-delay and partially unknown transition probabilities [C] . Shaohua Long, Shouming Zhong International Conference on Computing, Control and Industrial Engineering . 2012

机译：一类非线性单数马尔维亚跳跃系统随机受理，具有时滞和部分未知的过渡概率
5. Particle filtering for systems with unknown noise probability distributions. [D] . Xu, Shanshan. 2006

机译：具有未知噪声概率分布的系统的粒子滤波。
6. H∞ Estimation for Stochastic Time Delays in Networked Control Systems by Partly Unknown Transition Probabilities of Markovian Chains [O] . Chenyu Guo, Weidong Zhang -1

机译：H基于未知的马尔可夫链转移概率的网络控制系统随机时滞∞估计
7. Stabilization of Stochastic Markovian Jump Systems with Partially Unknown Transition Probabilities and Multiplicative Noise [O] . Yong Zhao, You Fu 2017

机译：具有部分未知的过渡概率和乘法噪声的随机马尔维亚跳跃系统的稳定化

Stabilization of Stochastic Markovian Jump Systems with Partially Unknown Transition Probabilities and Multiplicative Noise

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