增益随机变化随机丢包时滞系统非脆弱H∞滤波

鉴于目前的数字控制系统是离散的，设计了一类具有无穷分布时滞、随机丢失测量的离散系统的非脆弱H_∞滤波器．为了模拟离散系统增益随机变化现象，在滤波器的增益中引入高斯分布的随机变化分量；引入无穷分布时滞，刻画网络控制系统中有限的带宽产生的影响；进一步地，考虑由伯努利分布的白序列描述的随机丢失测量现象．基于李亚普诺夫稳定性理论、随机分析技术及线性矩阵不等式（LMI）技术，得到使整个滤波器增广系统渐近稳定，同时满足性能指标的非脆弱H_∞滤波器存在的充分条件，通过半定程序方法求解滤波器增益．最后，由数值仿真说明研究的有效性．

Non-fragile H∞ Filtering for Time-delay Systems with Random Gain Variations and Random Packet Dropouts

We design a non-fragile H_∞ filter for a class of discrete systems with infinite-distributed delays and randomly missing measurements. The proposal is made in consideration of the fact that current digital control systems are discrete ones. Random variables conformed to the Gaussian distribution are utilized in the gains of the filter to simulate the phenomenon of random gain variations in the discrete system. Infinite-distributed delays are then introduced to reflect the influence from the limited bandwidth in the networked control systems. Furthermore, the phenomenon of randomly missing measurements depicted by a Bernoulli distributed white sequence is considered. Based on Lyapunov stability theory, stochastic analysis technologyand LMI skills, the sufficient conditions for the existence of the non-fragile H_∞ filter are obtained. These conditions help make the filter error system asymptotically stable while simultaneously satisfying the performance index. As a result, the filter gains become solvable via the semi-definite programming technique. Finally, a numerical simulation is provided to illustrate the effectiveness of the research.