ℓ1-Induced filtering for discrete-time positive systems with interval uncertainties

We investigate the filter design problem for discretetime interval uncertain positive systems under the ℓ₁ performance in this paper. First, we propose some conditions expressed by linear programming to ensure the asymptotic stability and the ℓ₁ performance for given positive systems. Then, we establish a novel filter design approach and an iterative algorithm to obtain the desired filter for interval uncertain positive systems. To demonstrate the efficiency of the proposed controller design method, we provide a numerical example.