IEEE Trans Cybern. 2014 Mar;44(3):406-17. doi: 10.1109/TCYB.2013.2256782. Epub 2013 Aug 7.
In this paper, the H∞ fuzzy filtering problem is investigated for a class of discrete-time Takagi-Sugeno (T-S) fuzzy systems with randomly occurring uncertainties and randomly occurring interval time-varying delays, as well as channel fadings. A sequence of random variables obeying the Bernoulli distribution is utilized to govern the randomly occurring uncertainties and probabilistic interval time-varying delays. Simultaneously, the Rice fading model is employed to describe the phenomena of channel fadings by setting different values of the channel coefficients. Our attention is focused on the design of an H∞ fuzzy filter such that the filtering error dynamics is exponentially mean-square stable and the disturbance rejection attenuation is constrained to a given level by means of the H∞-performance index. In the presence of the randomly occurring phenomena, sufficient conditions are derived, via stochastic analysis and Lyapunov functional approach, for the existence of desired filter ensuring both the exponential mean-square stability and the prescribed H∞ performance. The filter parameters can be obtained by solving a convex optimization problem via the semidefinite program method. Finally, a numerical example is utilized to illustrate the usefulness and effectiveness of the proposed design technique.
本文针对一类具有随机发生不确定性和随机发生区间时变时滞以及信道衰落的离散时间 Takagi-Sugeno（T-S）模糊系统，研究了 H∞模糊滤波问题。利用服从伯努利分布的随机变量序列来控制随机发生的不确定性和概率区间时变时滞。同时，采用 Rice 衰落模型通过设置不同的信道系数值来描述信道衰落现象。我们关注的是设计一个 H∞模糊滤波器，使得滤波误差动力学具有指数均方稳定性，并且通过 H∞性能指标将干扰抑制衰减约束在给定水平。在存在随机发生现象的情况下，通过随机分析和 Lyapunov 函数方法推导出了存在所需滤波器的充分条件，该滤波器可以确保指数均方稳定性和规定的 H∞性能。通过半定规划方法求解凸优化问题可以得到滤波器参数。最后，通过一个数值实例说明了所提出设计技术的有用性和有效性。
