Delay-dependent H∞ filtering for singular Markov jump systems with Wiener process and generally uncertain transition rates

This paper is devoted to the investigation of the delay-dependent $ \mathrm {H}_{\infty } $ H∞ filtering problem for a class of continuous-time singular Markov jump systems with Wiener process and generally uncertain transition rates (GUTRs). In the GUTR stochastic singular model under consideration, based on an auxiliary vector function, by employing an integral inequality and some appropriate free-weighting matrices, the delay-dependent sufficient conditions are derived, which ensure that the filtering error system is stochastically admissible. And then, a singular filter is designed such that the filtering error system is not only regular, impulse-free and stochastically stable, but also satisfies a prescribed $ \mathrm {H}_{\infty } $ H∞ performance for all time-varying delays no larger than a given upper bound. Furthermore, the solvability conditions of the $ \mathrm {H}_{\infty } $ H∞ filtering problem are deduced in terms of a new type of candidate Lyapunov–Krasovskii function and a set of matrix inequalities. Finally, simulation examples are performed to validate the proposed method in this paper.