Optimal Disturbance Rejection with Zero Steady-state Error for Linear Discrete-time Systems

The problem of optimal disturbance rejection with zero steady-state error for linear discrete-time systems is considered. Based on the internal model principle, external persistent disturbance is compensated by constructing a disturbance compensator. Then, the optimal controller with an infinite-time horizon cost functional is designed by using classical optimal control theory, and the convergence of the cost functional can be guaranteed. A dynamic optimal feedback loop controller with zero steady-state error is obtained. A simulation example is given to test the validity of the presented algorithm