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Observer‐based controller for positive polynomial systems with time delay
Author(s) -
Iben Ammar Imen,
Gassara Hamdi,
El Hajjaji Ahmed,
Tadeo Fernando,
Chaabane Mohamed
Publication year - 2019
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.2542
Subject(s) - observer (physics) , control theory (sociology) , solver , positive definite matrix , polynomial , explained sum of squares , mathematics , state (computer science) , lyapunov function , controller (irrigation) , computer science , mathematical optimization , control (management) , algorithm , nonlinear system , mathematical analysis , eigenvalues and eigenvectors , quantum mechanics , physics , statistics , artificial intelligence , agronomy , biology
Summary This paper deals with some synthesis problems for a class of positive polynomial systems with time delay, for which the state vector takes nonnegative values whenever the initial conditions are nonnegative. First, the synthesis of state feedback controllers is solved using a Lyapunov‐Krasovskii approach, including the requirement of positiveness. In a second part, observers are included. In both cases, the design conditions are presented in terms of sum of squares, which can be numerically and symbolically solved via SOSTOOLS and a semidefinite program solver. Finally, four numerical examples are given to illustrate the proposed approach.