H∞ Filtering for 2-D Discrete-Time Periodic Markov Jump Systems With Multiplicative Noise: A Periodic HMM Approach
针对带乘性噪声和测量缺失的二维离散时间周期马尔可夫跳变系统，提出一种基于周期隐马尔可夫模型的异步H∞滤波器设计方法，保证滤波误差系统均方渐近稳定并满足指定干扰衰减性能。
This article presents the implementation of an asynchronous ${\mathcal {H}}_{\infty }$ filter for 2-D discrete-time periodic Markov jump systems with multiplicative noise. The study addresses the issue of missing measurements, which is treated as a stochastic variable following the Bernoulli random distribution. To account for the nonsynchronous phenomenon between the system and filter due to the loss of mode information, the periodic hidden Markov model (HMM) is introduced. Moreover, the transition rate matrix of the system and the conditional probability matrix of the filter are general, allowing for transition probabilities in fully known, partly known or fully unknown cases. The objective is to implement an asynchronous ${\mathcal {H}}_{\infty }$ filter based on periodic HMM that guarantees the filtering error system is mean-square asymptotically stable while maintaining a specified ${\mathcal {H}}_{\infty }$ disturbance attenuation performance. In the light of linear matrix inequalities, the article offers sufficient conditions for filter to exist and provides a solution for the parameters of the filter. Ultimately, a demonstration of the validity of the presented design technique is provided through the Darboux equation.