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This paper is concerned with optimal reference tracking control problem for discrete time 1-DOF/2-DOF systems. It is well known that l2 norm of an error, which is defined by difference between an output and a reference, does not turn zero for all possible controllers when plant is given as a non-minimum phase system. Purpose of this research is to derive closed-form expression of the optimal value of l2 norm of the error and its controller. The references for tracking are e.g. step, sine, impulse train, triangle wave and linear combination of these signals. Therefore, we can handle various signals as a reference. Moreover, our results can also characterize impact of the relative degree of plant. Those effectiveness are shown by numerical examples.

Closed-form Expression of Optimal Tracking Control Problem for Discrete Time Systems