H∞ filtering for discrete‐time singular nonhomogeneous Markovian jump systems with time‐varying delays

Abstract The work revisits the topic of filtering for discrete‐time singular nonhomogeneous Markovian jump systems (DSNMJSs) with time‐varying delays. An updated Lyapunov–Krasovskii functional (LKF) that has been discretely state‐decomposed is presented. This proposed LKF is used to derive some delay‐ and mode‐dependent sufficient conditions for the DSNMJSs. On this basis, a filtering error system that is causal and regular via applying a mode‐dependent filter is developed. A novel discrete state decomposition‐reorganization technology is then presented, which leads to the acquisition of the stochastically admissible condition. All of the planned filter's decomposition components are precisely calculated to determine the desired filter settings. It should be noted that the algorithm presented in this article increases the viability and flexibility of the filter settings. The strategy proposed in this work is shown to be superior to previous ones by the numerical findings, which also show that the offered results are less conservative and computationally complicated.