In this dissertation, a state-space methodology for optimal digital PID plus state-feedback controller design of analog transfer function matrices with multiple input-output time delays is proposed. The multiple time-delay transfer function matrix was minimally realized using continuous-time state equations with multiple input-output delays. To carry out digital design, the minimally realized state equation was discretized and represented as an extended discrete-time equation. Then, a partially pre-determined digital Proportional-Integral-Derivative (PID) controller and the afore-mentioned extended discrete-time state equation were formulated as an augmented discrete-time state-space model for state-feedforward and state-feedback Linear Quadratic Regulator (LQR) design. To implement the designed state-feedback controller and to reject the set-point disturbance, a new predictive discrete-time observer for the multivariable plant with multiple delays in input and output was constructed. Simulation examples were given to demonstrate the effectiveness of the proposed method and compare with alternative techniques. Closed-loop results show that this control design method provides good performance for the sampled-data systems with multiple time delays. The proposed approach is restricted to the time-delay systems where multiple time delays arise only in the input and output, and not in the state.