Finite-time $\mathcal {H}_{\infty }$H∞ filtering for Ito stochastic Markovian jump systems with distributed time-varying delays based on optimisation algorithm

This study is concerned with the problem of finite-time H-infinity filter design for a class of Ito stochastic systems with Markovian switching and distributed time-varying delays. Firstly, a partially mode-dependent filter is designed to accommodate to unreliable network transmission. The attention is focused on deriving sufficient conditions for the filtering error system to ensure the finite-time boundedness and to satisfy a prescribed H-infinity disturbance attenuation. Then based on stochastic functional theory, the existence of H-infinity filter is presented by solving existing linear matrix inequalities optimisation problems. Furthermore, the result is extended to the case where the mode information is completely transmitted. Finally, a numerical example is provided to show the effectiveness of the proposed results.