Event-triggered control design for networked evolutionary games with time invariant delay in strategies

This paper investigates the dynamics and control problem for a class of networked evolutionary games with time invariant delay (DNEGs) in strategies by using a semi-tensor product based method. A number of new results are presented. First, algebraic forms are constructed for DNEGs. Second, based on the algebraic formulations, necessary and sufficient conditions for the global convergence of desired strategy profile are presented under a state feedback event-triggered controller. Furthermore, the constructive procedure and the number of all valid event-triggered state feedback controllers are derived, which can make the game converge globally. Finally, an illustrative example is given to show the effectiveness of the obtained results.