Stability and Stabilization of State-Based Games

In this article, the convergence of state-based games (SBGs) with recurrent state equilibria is considered by the semi-tensor product of matrices. First, the state-action profile distribution is obtained by the proposed whole evolution equation of the state and the action profile. Second, two necessary and sufficient conditions are given to ensure the convergence of the SBGs, one of which is the matrix iteration condition and the other is a set of linear matrix inequalities. Then, the finite-time stabilization with probability one of the SBGs can be implemented by designing state feedback control. Finally, numerical simulations are given to verify the correctness of the theoretical results.