Positive filtering for positive Takagi–Sugeno fuzzy systems under ℓ1ℓ1 performance

In this paper, the positive filtering problem is addressed for positive Takagi–Sugeno (T–S) fuzzy systems under the ℓ1ℓ1-induced performance. To estimate the output of positive T–S fuzzy systems, error-bounding positive filters are constructed. A new performance characterization is first established to guarantee the asymptotic stability of the filtering error system with the ℓ1ℓ1-induced performance. Moreover, sufficient conditions expressed by linear programming problems are derived to design the required filters. Finally, a numerical example is presented to show the effectiveness of the derived theoretical results.