Discrete-time linear-quadratic output regulator for two variable systems

An augmented and minimum realization state space models of a two input two output plant are proposed for direct derivation of the discrete-time linear-quadratic regulator (DLQR) with measured not all the state variables but only the plant outputs. Both the models are related by means of original transformation based on the system modes. Using this transformation it is shown that the resulting closed-loop (CL) system with dynamic output feedback regulator (DOFR) has the same stable roots of its characteristic equation as the CL with state feedback regulator. It is shown that the observer appearing in DOFR is optimal and dead-beat. It is also shown that the CL system with DOFR realizes the optimal LQ control of the system with feedback from the augmented state.