Finite-time stabilization for nonlinear discrete-time singular Markov jump systems with piecewise-constant transition probabilities subject to average dwell time
Finite-time stabilization for nonlinear discrete-time singular Markov jump systems with piecewise-constant transition probabilities subject to average dwell time
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具有分段常数转移概率的非线性离散时间奇异马尔可夫跳跃系统的有限时间稳定性
DOI：
10.1016/j.jfranklin.2017.01.014
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发表时间：
2017-03
期刊：
影响因子：
--
通讯作者：
Chenghui Zhang
中科院分区：
文献类型：
--
作者：
Jimin Wang;Shuping Ma;Chenghui Zhang
本文首次研究了具有平均停留时间切换的时变跃迁概率非线性离散奇异马尔可夫跳变系统的有限时间有界性和镇定问题。考虑了跃迁概率的有限分段齐次特性。首先，利用平均停留时间方法和隐函数定理，给出了非线性离散奇异马尔可夫跳变系统是奇异有限时间有界且有唯一解的充分条件；其次，根据奇异值分解方法，提出了线性矩阵不等式有限时间有界准则，该准则可直接用于构造状态反馈控制器。基于这一LMI有限时间有界准则，进行了状态反馈控制器的设计。最后给出了三个数值算例，说明了所提方法的有效性和优越性。
In this paper, the finite-time boundedness and stabilization issues for nonlinear discrete-time singular Markov jump systems with time-varying transition probabilities subject to average dwell time switching are studied for the first time. The finite piecewise homogeneous character of transition probabilities is taken into account. Firstly, by using average dwell time approach and implicit function theorem, a sufficient condition is presented such that the nonlinear discrete-time singular Markov jump systems are singular finite-time bounded and of a unique solution. Secondly, according to the singular value decomposition approach, a linear matrix inequality (LMI) finite-time boundedness criterion is developed, which can be used for constructing state feedback controllers directly. Based on this LMI finite-time boundedness criterion, the state feedback controller design is handled. Finally, three numerical examples are presented to illustrate the validity and advantage of the proposed methods.
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