New approach to delay-dependent H∞ control for continuous-time Markovian jump systems with time-varying delay and deficient transition descriptions
New approach to delay-dependent H∞ control for continuous-time Markovian jump systems with time-varying delay and deficient transition descriptions
复制标题
DOI：
10.1016/j.jfranklin.2014.10.022
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Jianbin Qiu;Yanling Wei;H. Karimi
中科院分区：
文献类型：
--
作者：
Jianbin Qiu;Yanling Wei;H. Karimi
针对一类连续时间马尔可夫跳变线性系统（MJLS），提出了一种基于输入输出（IO）的时滞相关稳定性分析和H∞控制器设计方法.所研究的系统具有时变时滞和马尔可夫随机过程中的模式信息不足，同时涉及精确已知、部分未知和不确定的转移率。首先证明了具有时变时滞的原系统可以通过一个新的IO模型通过两项近似的过程重新表示，原系统的稳定性问题可以转化为IO模型的缩放小增益（SSG）问题。然后，基于马尔可夫Lyapunov-Krasovskii的SSG条件和一些凸化技术，以线性矩阵不等式的形式给出了MJLS的稳定性分析和状态反馈H∞控制器的综合条件.仿真研究表明了所提出的分析和设计方法的有效性和优越性。
This paper proposes an input–output (IO) approach to the delay-dependent stability analysis and H∞ controller synthesis for a class of continuous-time Markovian jump linear systems (MJLSs). The concerned systems are with a time-varying delay in the state and deficient mode information in the Markov stochastic process, which simultaneously involves the exactly known, partially unknown and uncertain transition rates. It is first shown that the original system with time-varying delay can be reformulated by a new IO model through a process of two-term approximation and the stability problem of the original system can be transformed into the scaled small gain (SSG) problem of the IO model. Then, based on a Markovian Lyapunov–Krasovskii formulation of SSG condition together with some convexification techniques, the stability analysis and state-feedback H∞ controller synthesis conditions for the underlying MJLSs are formulated in terms of linear matrix inequalities. Simulation studies are provided to illustrate the effectiveness and superiority of the proposed analysis and design methods.