Delay-dependent H∞ filtering for discrete-time singular Markovian jump systems with time-varying delay and partially unknown transition probabilities
Delay-dependent H∞ filtering for discrete-time singular Markovian jump systems with time-varying delay and partially unknown transition probabilities
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DOI：
10.1016/j.sigpro.2010.07.005
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发表时间：
2011-02
期刊：
影响因子：
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通讯作者：
Jinxing Lin;S. Fei;Jiong Shen
中科院分区：
文献类型：
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作者：
Jinxing Lin;S. Fei;Jiong Shen
本文研究了一类时变时滞和部分未知转移概率的离散时间奇异马尔可夫跳跃系统的H∞滤波设计。所考虑的系统类别更为一般，涵盖了具有完全已知和完全未知转移概率作为两种特殊情况的奇异马尔可夫延迟系统。构建了一个依赖于模式的滤波器，并通过定义适当的随机 Lyapunov 函数并结合使用离散 Jensen 不等式，根据线性矩阵不等式 (LMI) 建立了所考虑系统的依赖于延迟的有界实数引理 (BRL)。在此基础上，采用LMI技术给出了所需滤波器存在的充分条件，保证了相应滤波误差系统的可容许性和H∞性能。提供了一些数值例子来说明所开发的理论结果的有效性。
This paper is concerned with the H∞filtering design for a class of discrete-time singular Markovian jump systems with time-varying delay and partially unknown transition probabilities. The class of systems under consideration is more general and covers the singular Markovian delay systems with completely known and completely unknown transition probabilities as two special cases. A mode-dependent filter is constructed and by defining an appropriate stochastic Lyapunov functional combined with using the discrete Jensen inequality, a delay-dependent bounded real lemma (BRL) for the considered systems is established in terms of linear matrix inequalities (LMIs). Based on this, a sufficient condition on the existence of the desired filter which guarantees the admissibility and the H∞performance of the corresponding filtering error system is presented by employing the LMIs technique. Some numerical examples are provided to illustrate the effectiveness of the developed theoretical results.