Finite-Time $$H_{\infty }$$H∞ Filtering for Discrete-Time Piecewise Homogeneous Markov Jump Systems with Missing Measurements

The problem of finite-time $$H_{\infty }$$H∞ filtering is studied for discrete-time Markov jump systems with time-varying transition probabilities and missing measurements. The time-varying TPs are assumed to be finite piecewise homogenous and the missing measurements phenomenon is modelled as a Bernoulli distributed sequence. An $$H_{\infty }$$H∞ filter is designed to estimate the unmeasured state and achieve a prescribed $$H_{\infty }$$H∞ performance level. The sufficient criteria are derived to guarantee the filtering error system to be finite-time bounded. Finally, a simulation example is presented to demonstrate the applicability of the obtained results.