This paper is devoted to the characterization of existence and uniqueness conditions for the stabilizing solution of a large class of Riccati equations arising in stochastic dynamic games. As an application of the obtained results, we consider in a second step the problem of a zero-sum two players linear quadratic difference game for a stochastic discrete-time dynamical system subject to both random switching of its coefficients and multiplicative noise. We show that in the solution of such a control problem, a crucial role is played by the stabilizing solution of the considered class of Riccati difference equations.

中文翻译：

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论一类周期随机Riccati方程稳定解的存在性


本文致力于描述随机动态博弈中出现的一类 Riccati 方程稳定解的存在性和唯一性条件。作为所获得结果的应用，我们在第二步中考虑随机离散时间动力系统的零和双玩家线性二次差分博弈问题，该系统受到其系数的随机切换和乘性噪声的影响。我们表明，在解决此类控制问题时，所考虑的 Riccati 差分方程类的稳定解发挥着至关重要的作用。