State‐bounding observer design for uncertain positive systems under ℓ 1 performance

Summary This paper investigates the ℓ 1 ‐induced positive observer design problem for uncertain positive systems. First, we present the ℓ 1 ‐induced performance indicator for positive systems, which fits well into the linear Lyapunov function. Then, a novel ℓ 1 ‐induced performance characterization is developed for uncertain positive systems. Furthermore, a linear programming–based method is proposed to solve the ℓ 1 ‐induced positive observer synthesis problem for positive systems with interval uncertainties. A pair of positive state‐bounding observers is designed to estimate the state of uncertain positive systems. Finally, we provide a numerical example to demonstrate the validity and efficiency of the derived methods.