Time delay is inevitable in information communication. Switched time delay, as a time-varying delay, plays an important role in information interaction between agents. In this article, networked evolutionary games (NEGs) with switched time delay are investigated, including modeling and dynamics analysis. First, the dynamic model of the delayed NEG is proposed, then the algebraic formulation is established by using the algebraic state-space approach. Second, dynamic behavior of the game is discussed, involving general convergence and evolutionarily stable profile analysis. Necessary and sufficient conditions are derived for convergence of the game and evolutionarily stable profile, respectively. Finally, two illustrative examples are employed to demonstrate the validity of the theoretical results.

In this study, the output tracking of delayed logical control networks (DLCNs) with state and control constraints is further investigated. Compared with ot

This paper investigates the set stabilization of networked evolutionary games (NEGs) with probabilistic time-varying delays (PTDs). Utilizing the algebraic state space approach, a unified algebraic framework is constructed to investigate the evolutionary game with arbitrary network structures and probabilistic delays. Based on the algebraic formulation, set stability of NEGs with PTDs is studied first and a necessary and sufficient condition is proposed to characterize the set stability. Then, set stabilization of NEGs with PTDs is investigated via the truth matrix method, including the derivation of verification conditions and the design of controller. Finally, an example is carried out to illustrate the theoretical results.

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.