A unified filter for singular Markovian jump systems with mixed delays based on an extended free-matrix-based inequality approach

In this article, the problem of unified filters design including H_∞ , L₂ − L_∞ , passive, dissipative filters and their reduced-order ones is addressed for continuous-time singular Markovian jump systems with discrete and distributed delays. Unlike some existing works, the mixed delays can be fully captured by proposing an extended free-matrix-based integral inequality. By considering two cases of distributed delays, two novel criteria are presented to ensure the filtering error system to be stochastically admissible and extended dissipative. Some numerical examples are provided to illustrate the effectiveness of the unified filter design methods.