Reduced-order ℓ₂-ℓ_∞ filtering for discrete-time T-S fuzzy systems with stochastic perturbation

This paper is concerned with the problem of ℓ₂-ℓ_∞ filtering for discrete-time Takagi-Sugeno (T-S) fuzzy systems with stochastic perturbation. Firstly, a basis-dependent existence condition of desirable ℓ₂-ℓ_∞ filters is proposed. Then by means of the convex linearisation technique, the derived condition is transformed into some strict linear matrix inequality (LMI) constraints, by which both full-and reduced-order filters can be designed. Moreover, for the reduced-order ℓ₂-ℓ_∞ filter design, a novel analysis and design method with the projection lemma is also provided. Finally, a numerical example is provided to illustrate the feasibility and effectiveness of the proposed full-and reduced-order ℓ₂-ℓ_∞ filter design methods.