Optimal disturbance rejection for discrete-time nonlinear systems with time-delays via high-gain observer-based control

The discrete-time mathematical models for nonlinear systems with delayed control and measurement are established. Based on a linearization and a model transformation, the nonlinear system with delays is transformed to a formal nondelay system. Then the optimal control law with the state feedback term, the disturbance feedforward term, and the control memory term is derived from a discrete Riccati equation and a Stein equation. A high-gain observer is constructed such that the feedforward control law is physically realizable. Simulation results demonstrate the effectiveness of the optimal control law.