Set Stabilization of Networked Evolutionary Games With Probabilistic Time-Varying Delays

This article 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, the set stability of NEGs with PTDs is studied first, and a necessary and sufficient condition is proposed to characterize the set stability. Then, the set stabilization of NEGs with PTDs is investigated via the truth matrix method, including the derivation of verification conditions and the design of the controller. Finally, an example is carried out to illustrate the theoretical results.