H-infinity model reduction for continuous-time Markovian jump systems with incomplete statistics of mode information
H-infinity model reduction for continuous-time Markovian jump systems with incomplete statistics of mode information
复制标题
模态信息不完全统计的连续时间马尔可夫跳跃系统的H无穷模型简化
DOI：
10.1080/00207721.2013.837545
复制
发表时间：
2014
影响因子：
4.3
通讯作者：
Wang Mao
中科院分区：
文献类型：
--
作者：
Wei Yanling;Qiu Jianbin;Karimi Hamid Reza;Wang Mao
研究了一类连续时间马尔可夫跳变线性系统的模型降阶问题，该系统具有模式信息不完全统计，同时考虑了转移率的精确已知、部分未知和不确定性.通过充分利用转移率矩阵的性质，结合不确定域的凸化，首先导出了一个新的性能分析的充分条件，然后提出了两种求解模型降阶问题的方法，即凸线性化方法和迭代方法.结果表明，所需的降阶模型可以通过求解一组严格的线性矩阵不等式（LMI）或序列最小化问题的LMI约束，这是数值上有效的商用软件。最后，通过一个算例验证了所提方法的有效性.
This paper investigates the problem of model reduction for a class of continuous-time Markovian jump linear systems with incomplete statistics of mode information, which simultaneously considers the exactly known, partially unknown and uncertain transition rates. By fully utilising the properties of transition rate matrices, together with the convexification of uncertain domains, a new sufficient condition for performance analysis is first derived, and then two approaches, namely, the convex linearisation approach and the iterative approach, are developed to solve the model reduction problem. It is shown that the desired reduced-order models can be obtained by solving a set of strict linear matrix inequalities (LMIs) or a sequential minimisation problem subject to LMI constraints, which are numerically efficient with commercially available software. Finally, an illustrative example is given to show the effectiveness of the proposed design methods.