Reduced-order filter design for discrete-time Takagi-Sugeno fuzzy stochastic systems

This work focuses on the problem of full- and reduced-order ℓ₂-ℓ_∞ filter design for discrete-time Takagi-Sugeno (T-S) fuzzy stochastic systems. Firstly, we propose a basis-dependent condition for the existence of desirable ℓ₂-ℓ_∞ filters. Then by the convex linearization technique, we transform the derived condition into some strict linear matrix inequality (LMI) constraints. At the same time, both full- and reduced-order filters can be designed by solving those LMIs. What´s more, based on the projection lemma, we also provided a novel analysis method for the reduced-order ℓ₂-ℓ_∞ filter design. Finally, the feasibility of the proposed full- and reduced-order ℓ₂-ℓ_∞ filter design methods is verified by a numerical example.