Sign-indefinite linear quadratic differential game for stochastic systems via static output feedback strategy

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.