Finite-Time Extended Dissipative Filtering for Singular T–S Fuzzy Systems With Nonhomogeneous Markov Jumps

This article investigates the finite-time extended dissipative filtering for singular T–S fuzzy Markov jump systems with time-varying transition probabilities (TPs). The time-varying TPs are considered to reside in a polytope. By resorting to a generalized performance index, the
$H_{\infty }$
,
$L_{2}-L_{\infty }$
, passive, and dissipative performance can be solved in a unified framework. Combining the free-weighting method and the proposed recursive method, a sufficient condition on singular stochastic extended dissipative finite-time boundedness (SSEDFTB) for a fuzzy filtering error system is obtained. By proposing a decoupling principle called double variables-based decoupling principle (DVDP) and a variable substitution principle (VSP), a novel condition on the existence of the fuzzy filter is presented in terms of linear matrix inequalities (LMIs). Compared with the existing works, the assumption on state variables and the constraints of slack matrices are overcome, which leads to more practical and less conservative results. A practical example is provided to demonstrate the effectiveness of the design methods.