H∞ Filter for Discrete-Time Periodic Piecewise Systems With Missing Measurements
研究了测量数据随机缺失下离散时间周期分段系统的H∞滤波器设计，通过伯努利过程建模缺失，构造带周期参数的连续李雅普诺夫函数，给出了保证滤波误差系统均方指数稳定和H∞性能的充分条件，并针对无缺失情形用不连续李雅普诺夫函数开发了性能更优的标称滤波器。
In this article, the H∞ filter design for discrete-time periodic piecewise systems with missing measurements is studied. First, a Bernoulli process is used to characterize missing measurements. Then, by constructing the continuous Lyapunov function with discrete time-scheduling periodic parameters, under missing measurements, sufficient conditions are obtained to ensure the exponential mean-squared stability and H∞ estimation performance of the periodic piecewise filtering error system (PPFES). Moreover, in the case of complete transmission (no missing case), a nominal H∞ filter with more superior performance is developed by the discontinuous Lyapunov function, which provides a complement for the tradeoff between filter schemes with and without missing measurements. Finally, numerical examples are applied to certify the effectiveness of our method.