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Robust preview control for uncertain discrete‐time systems based on LMI
Author(s) -
Liao Fucheng,
Li Li
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.2308
Subject(s) - control theory (sociology) , linear matrix inequality , controller (irrigation) , mathematics , robust control , integrator , computer science , discrete time and continuous time , matrix (chemical analysis) , tracking error , full state feedback , operator (biology) , control system , mathematical optimization , control (management) , engineering , artificial intelligence , materials science , computer network , bandwidth (computing) , composite material , biology , agronomy , statistics , electrical engineering , repressor , chemistry , biochemistry , transcription factor , gene
Summary For a class of uncertain discrete‐time systems, a preview controller based on linear matrix inequality is proposed. A new method is derived to construct an augmented error system instead of taking the difference of the error signal and the system equation. The new approach avoids applying the difference operator to the time‐varying matrix and can simplify the augmented error system. For the augmented error system of the uncertain system, state feedback is introduced. The sufficient condition of asymptotic stability of the closed‐loop system is derived for the performance index by using the relevant theorems of robust control theory. The condition can be realised by solving a linear matrix inequality optimization problem. By incorporating the controller obtained into the original system, we obtain the preview controller. Moreover, introducing an integrator allows the closed‐loop system to robustly track the desired tracking signal without steady‐state error.