Stability and Stabilization of State-Based Games
研究了基于状态的博弈中状态-动作分布收敛的条件，通过矩阵半张量积提出演化方程，给出两个充要条件，并设计状态反馈控制实现有限时间镇定。
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.