ℓ1-induced state-bounding observer design for positive Takagi-Sugeno fuzzy systems

In this paper, the design problem of the ℓ1-induced positive observer is studied for positive Takagi-Sugeno (T-S) fuzzy systems. First, a ℓ1-induced performance index is presented for positive systems and the performance indicator matches well to the linear Lyapunov functions. Then, we explore a novel description of the ℓ1-induced performance for positive T-S fuzzy systems. Moreover, the design problem of the ℓ1-induced positive observer is solved for positive fuzzy systems under a proposed linear programming method. To estimate the state of positive fuzzy systems, a couple of state-bounding positive observers are constructed. In the end, a numerical example is given to show the effectiveness of the proposed approach.