On Robust Stability and Stabilization of Networked Evolutionary Games with Time Delays

This paper investigates the robust stability and stabilization of networked evolutionary games (NEGs) with time delays. First, a mathematical model is presented to describe the dynamics of NEG with time-varying delays and disturbances. Second, an auxiliary system is constructed using the semi-tensor...

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Bibliographic Details
Published inMathematics (Basel) Vol. 10; no. 15; p. 2695
Main Authors An, Qiguang, Guo, Hongfeng, Zheng, Yating
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.08.2022
Subjects
Algebra
Algorithms
Control systems design
Control theory
Cooperation
disturbance
Equilibrium
Game theory
Games
Mathematical analysis
networked evolutionary games
Research methodology
robust stability and stabilization
Robust stabilization
semi-tensor product of matrices
Stability augmentation
Tensors
time delays
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Summary:This paper investigates the robust stability and stabilization of networked evolutionary games (NEGs) with time delays. First, a mathematical model is presented to describe the dynamics of NEG with time-varying delays and disturbances. Second, an auxiliary system is constructed using the semi-tensor product of matrices and a dimension augmenting technique. Then, a verification condition of robust stability is derived. Third, in order to stabilize NEG to the Nash equilibrium, the robust stability problem is transformed into the robust stabilization problem. Moreover, an algorithm is proposed to design the stabilization controller. Finally, the validity of the results is verified by an example.
ISSN:2227-7390
2227-7390
DOI:10.3390/math10152695