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State‐bounding observer design for uncertain positive systems under ℓ 1 performance
Author(s) -
Chen Xiaoming,
Chen Mou,
Shen Jun
Publication year - 2017
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2360
Subject(s) - bounding overwatch , positive systems , observer (physics) , control theory (sociology) , interval (graph theory) , lyapunov function , linear programming , mathematics , state (computer science) , mathematical optimization , function (biology) , state observer , linear system , computer science , nonlinear system , algorithm , artificial intelligence , physics , control (management) , quantum mechanics , mathematical analysis , combinatorics , evolutionary biology , biology
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.