H∞ Filter for Discrete-Time Periodic Piecewise Systems With Missing Measurements

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.