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This study focuses on the problem of optimal mismatched disturbance rejectioncontrol for uncontrollable linear discrete-time systems. In contrast toprevious studies, by introducing a quadratic performance index such that theregulated state can track a reference trajectory and minimize the effects ofdisturbances, mismatched disturbance rejection control is transformed into alinear quadratic tracking problem. The necessary and sufficient conditions forthe solvability of this problem over a finite horizon and a disturbancerejection controller are derived by solving a forward-backward differenceequation. In the case of an infinite horizon, a sufficient condition for thestabilization of the system is obtained under the detectable condition. Thispaper details our novel approach to disturbance rejection. Four examples areprovided to demonstrate the effectiveness of the proposed method.

An Approach to Mismatched Disturbance Rejection Control for Uncontrollable Systems