Finite-time unbiased H∞H∞ filtering for discrete jump time-delay systems

In this paper, the finite-time unbiased H∞H∞ filtering analysis is conducted for discrete time-delay systems with both Markovian jump parameters and norm-bounded external disturbance. The definitions of stochastic finite time boundedness and stochastic finite-time unbiased H∞H∞ filtering are first given. Then, by using the unbiased estimation approach, sufficient conditions for stochastic H∞H∞ finite-time boundedness are derived. Based on linear matrix inequality technique, an unbiased H∞H∞ filter is designed to guarantee stochastic H∞H∞ finite-time boundedness of the resulting unbiased filtering error dynamics. Moreover, the design method of finite-time unbiased H∞H∞ filtering is presented for discrete jump systems without time delay. In sequel, the related optimization problems are also provided to minimize the required performance level. Finally, two numerical examples are exploited to demonstrate the validity of the obtained results.