Dynamic compensator design for discrete-time LQG problem using Markov parameters

This paper considers the discrete-time LQG control system design based on the input-output data using Markov parameters for system representation. The approach is based on the time series treatment. In the first step, for the system described in the state space settings, we derive the closed-form solutions of the optimal control and the optimal filter gains. In the next step, we show that those closed-form solutions reduce to the recursive forms of Riccati equations. Finally, combining the closed-form solutions, an LQG control law is designed in the form of the dynamic compensator using Markov parameters of the plant