Premium
Stabilization of positive coupled differential‐difference equations with unbounded time‐varying delays
Author(s) -
Liu Guomin,
Zhao Ping,
Li Ruonan
Publication year - 2020
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.2663
Subject(s) - control theory (sociology) , stability (learning theory) , mathematics , controller (irrigation) , differential (mechanical device) , state (computer science) , full state feedback , differential equation , control (management) , computer science , mathematical analysis , engineering , algorithm , agronomy , biology , aerospace engineering , artificial intelligence , machine learning
Summary This paper researches the static output‐feedback stabilization of single‐input single‐output (SISO) positive coupled differential‐difference equations (CDDEs) with unbounded time‐varying delays. First, a necessary and sufficient condition is provided for the positivity and asymptotical stability of CDDEs with unbounded time‐varying delays. For this type of system, based on the constructed estimates of its solution, a necessary and sufficient condition on asymptotical stability is provided. Then, based on this criterion, for CDDEs with unbounded time‐varying delays, a kind of static output‐feedback controller is designed to ensure the positivity and asymptotical stability of the corresponding closed‐loop systems. It is also worth pointing out that the controller is designed by the linear programming method without parameterization technique. This design approach can also be applied to the static state feedback stabilization problem of CDDEs with unbounded time‐varying delays. Finally, two illustrative examples are given to show the effectiveness of our results.