Robust H∞ filtering for singular Markovian jump systems via decoupling and substitution principles

This paper extends the existing results on the robust H∞ filtering problem for singular Markovian jump systems. Firstly, the double variables‐based decoupling principle and the variable substitution principle are proposed, respectively. Secondly, the two principles are employed to formulate a robust H∞ filter design condition, which ensures the filtering error system to be stochastically admissible and meet H∞ performance. Compared with the existing works, this paper fully considers the free structure of introduced slack matrices, which provides extra dimensions in the solution space. It directly leads to the reduction of conservativeness in the filtering solution. The effectiveness of the proposed methods is illustrated by a numerical example.