部分转移概率未知的时滞离散Markov跳变系统可达集估计

林文娟,何勇

系统科学与数学 ›› 2019, Vol. 39 ›› Issue (2) : 298-310.

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PDF(470 KB)
系统科学与数学 ›› 2019, Vol. 39 ›› Issue (2) : 298-310. DOI: 10.12341/jssms13589
论文

部分转移概率未知的时滞离散Markov跳变系统可达集估计

    林文娟,何勇
作者信息 +

Reachable Set Estimation for Delayed Discrete-Time Markov Jump Systems with Partially Unknown Transition Probabilities

    LIN Wenjuan ,HE Yong
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摘要

针对一类具有部分转移概率未知的时滞离散Markov跳变系统, 文章研究了其可达集估计问题. 构造一个时滞依赖的Lyapunov函数, 利用改进逆凸矩阵不等式, Jensen 求和不等式, 自由权矩阵方法等技术对Lyapunov函数的前向差分进行估计, 并使用等价变换处理未知转移概率相关项, 从而获得系统可达集存在的充分条件. 最后, 通过数值实例验证了所提方法的有效性与优越性.

Abstract

This paper is concerned with the problem of reachable set estimation for discrete-time Markov jump systems with time-varying delays and partially unknown transition probabilities. By constructing a delay-dependent Lyapunov functional, utilizing the extended reciprocally convex matrix inequality, Jensen summation inequality, and the free matrix weighting approach to estimate the forward difference of the constructed Lyapunov functional, and using an equivalent transformation method to deal with the unknown transition probabilities related terms, sufficient condition that guaranteeing the existence of an ellipsoidal reachable set is established. Finally, a numerical example with simulation results is given to demonstrate the effectiveness and superiority of the proposed results.

关键词

Markov跳变系统 / 时滞 / 可达集估计 / Lyapunov函数.

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林文娟 , 何勇. 部分转移概率未知的时滞离散Markov跳变系统可达集估计. 系统科学与数学, 2019, 39(2): 298-310. https://doi.org/10.12341/jssms13589
LIN Wenjuan , HE Yong. Reachable Set Estimation for Delayed Discrete-Time Markov Jump Systems with Partially Unknown Transition Probabilities. Journal of Systems Science and Mathematical Sciences, 2019, 39(2): 298-310 https://doi.org/10.12341/jssms13589
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