A discrete-time coupled state dependent Riccati equation control strategy is structured in this manuscript for synthesizing state feedback controllers satisfying the combined nonlinear quadratic regulator and H_infinity robust control performance objectives. Under smoothness assumptions, the nonlinear plant dynamics can be formulated into state-dependent coefficient form through direct parameterization. By solving a pair of coupled state-dependent Riccati equations, the optimal stabilizing solutions can achieve inherent stability, nonlinear quadratic optimality, and H_infinity disturbance attenuation performance. The established two-player Nash's game theory is utilized for developing both of the finite- and infinite-time optimal control laws. Furuta swing-up pendulum, a representative nonholonomic underactuated nonlinear system, is stabilized in real-time for validating the robustness and potential of proposed approach in mechatronics applications.