Finite-time H∞ filtering for discrete-time Markovian jump systems

This paper investigates the problem of finite-time H∞ filtering for one class of discrete-time Markovian jump systems with time-varying norm-bounded disturbance. Firstly, the filtering error dynamic system is constructed based on an H∞ filter with or without the control input. Then, an H∞ filtering is designed to ensure stochastic finite-time boundedness of the resulting filtering error system and satisfying a prescribed H∞ attenuation level for the filtering error system in the given finite-time interval. Sufficient criteria on the stochastic H∞ finite-time boundedness are established in terms of linear matrix inequalities with a fixed parameter. As an auxiliary result, we also tackle the problem of finite-time H∞ filtering for discrete-time Markovian jump systems without the control input and provide sufficient conditions on finite-time H∞ filtering for the family of discrete-time Markovian jump systems. Finally, numerical examples are presented to show the validity of the developed techniques.