State‐bounding observer design for uncertain positive systems under ℓ1 performance

Summary This paper investigates the l1-induced positive observer design problem for uncertain positive systems. First, we present the l1-induced performance indicator for positive systems, which fits well into the linear Lyapunov function. Then, a novel l1-induced performance characterization is developed for uncertain positive systems. Furthermore, a linear programming–based method is proposed to solve the l1-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.

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