A discrete-time-coupled state-dependent Riccati equation (CSDRE) control strategy is structured in this paper for synthesizing state feedback controllers satisfying the combined nonlinear quadratic regulator (NLQR) and 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 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.