Sign-indefinite linear quadratic differential game for stochastic systems by means of static output feedback (SOF) strategy is investigated. First, the saddle point equilibrium condition of external disturbance and control strategy is established based on stochastic cross-coupled algebraic matrix equations (SCCAMEs). Second, the numerical algorithms for solving the SCCAMEs are discussed. In particular, the difference between the existing algorithm and the proposed one is addressed. In order to show the validity for the several algorithms, a modified practical numerical example is demonstrated. In particular, it is shown that the optimality for the cost functional cannot be attained via the existing algorithm. Furthermore, it is claimed that the new proposed algorithm by combining the numerical algorithm that consist of stochastic Ricatti and Lyapunov equations with the Newton method is useful and reliable because the setting of the initial condition is quite easy task and fast convergence is attained.

中文翻译：

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通过静态输出反馈策略的随机系统的符号不定线性二次微分博弈

研究了采用静态输出反馈（SOF）策略的随机系统的符号不定线性二次微分博弈。首先，基于随机交叉耦合代数矩阵方程（SCCAME）建立外部扰动的鞍点平衡条件和控制策略。其次，讨论了求解 SCCAME 的数值算法。特别是，解决了现有算法和所提出的算法之间的差异。为了证明几种算法的有效性，演示了一个修改后的实际数值例子。特别是，它表明通过现有算法无法获得成本函数的最优性。此外，