Stabilisation of Markov jump linear systems subject to both state and mode detection delays
Stabilisation of Markov jump linear systems subject to both state and mode detection delays
复制标题
DOI：
10.1049/iet-cta.2013.0507
复制
发表时间：
2014-03
影响因子：
2.6
通讯作者：
Ting Yang;Lixian Zhang;Yuandi Li;Yusong Leng
中科院分区：
文献类型：
--
作者：
Ting Yang;Lixian Zhang;Yuandi Li;Yusong Leng
研究了一类具有时滞的离散马尔可夫跳跃线性系统的镇定问题，该时滞同时发生在系统状态和模式检测中。模式检测延迟意味着在系统模式的切换和相应控制器的切换之间存在滞后。状态延迟被认为是随机的，但有上下界，并且模式检测延迟被假设为常数。通过扩展状态空间，可以将底层系统建模为马尔可夫跳跃线性系统，其中系统复杂度和系统模式数都有不同程度的增加，但当模式检测延迟变大时保持不变。利用修正的随机Lyapunov函数，得到了系统随机稳定的充分条件。数值算例验证了所提设计方法的有效性。
This study addresses the stabilisation problem of a class of discrete-time Markov jump linear systems subject to time delays which occur in both the system state and mode detection. The mode detection delay means that there exists a lag between the switching of the system modes and the switching of the corresponding controllers. The state delays are considered to be random but with upper and lower bounds, and the mode detection delay is assumed to be constant. With an extended state space, the underlying system can be remodelled as a Markov jump linear system in which the system complexity and the number of system modes are both increased to a certain extent, but remain unchanged when the mode detection delay becomes larger. A sufficient condition guaranteeing the stochastic stability of the system is obtained via a modified stochastic Lyapunov function. The effectiveness of the proposed design approach is demonstrated by a numerical example.