A delay decomposition approach to L2-Linfinity filter design for stochastic systems with time-varying delay
A delay decomposition approach to L2-Linfinity filter design for stochastic systems with time-varying delay
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DOI：
10.1016/j.automatica.2011.02.021
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发表时间：
2011-07
期刊：
影响因子：
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通讯作者：
Huai‐Ning Wu;Jun‐Wei Wang;P. Shi
中科院分区：
文献类型：
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作者：
Huai‐Ning Wu;Jun‐Wei Wang;P. Shi
本文研究了一类时变时滞随机系统的L2-L∞滤波器设计问题。解决的问题是设计一个全阶线性滤波器，使误差系统渐近均方稳定并满足规定的 L2–L∞ 性能。为了开发不太保守的滤波器设计，通过将延迟区间分解为多个等距子区间来构造新的Lyapunov-Krasovskii泛函（LKF），并在随机设置下建立新的积分不等式。然后，基于LKF和积分不等式，以线性矩阵不等式（LMI）的形式获得了L2-L∞滤波器存在的延迟相关条件。由此产生的滤波器可以确保误差系统是渐近均方稳定的，并且估计误差的峰值受到所有可能的有界能量扰动的规定水平的限制。最后，给出两个例子来说明所提方法的有效性。
This paper investigates the problem of L2–L∞filter design for a class of stochastic systems with time-varying delay. The addressed problem is the design of a full order linear filter such that the error system is asymptotically mean-square stable and a prescribed L2–L∞performance is satisfied. In order to develop a less conservative filter design, a new Lyapunov-Krasovskii functional (LKF) is constructed by decomposing the delay interval into multiple equidistant subintervals, and a new integral inequality is established in the stochastic setting. Then, based on the LKF and integral inequality, the delay-dependent conditions for the existence of L2–L∞filters are obtained in terms of linear matrix inequalities (LMIs). The resulting filters can ensure that the error system is asymptotically mean-square stable and the peak value of the estimation error is bounded by a prescribed level for all possible bounded energy disturbances. Finally, two examples are given to illustrate the effectiveness of the proposed method.