Abstract
摘要: 研究了在观测中存在Markov跳跃时滞的离散时间系统的线性最小方差状态估计问题. 首先, 通过引入跳跃时滞的示性函数, 将带有跳跃时滞的观测方程转化为带有乘性噪声的定常时滞系统. 进一步采用状态扩维的方法, 将定常时滞系统转化为无时滞的Markov跳跃系统. 最后, 基于得到的无时滞系统, 采用Hilbert空间已有的几何论知识, 设计线性最优状态估计器, 得出基于Riccati方程的滤波器的表达式, 并证明了所得滤波器的渐渐收敛性. 关键词: 线性估计 / 离散时间系统 / Markov跳跃时滞 / Riccati方程
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