Positive state-bounding observer for interval positive systems under L1 performance

In this paper, the positive observer problem is investigated for interval positive systems under the L₁-induced performance. To estimate the state of positive systems, a pair of state-bounding positive observers is designed. A novel characterization is first proposed under which the augmented system is stable and satisfies the L₁-induced performance. Necessary and sufficient conditions are then presented to design the observers. The results obtained in this paper are expressed in terms of linear programming problems, and can be easily solved by standard software. In the end, we present a numerical example to show the effectiveness of the derived design procedures.