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The two-delay input control proposed by Mita et al is attractive since it makes it possible to solve problems connected with unstable zeros. It is a digital control system in which control inputs are changed twice in a sampling period. The two-delay input control was shown to have no zeros. In this paper, the assumption on the zero of the basic discrete-time system is relaxed. That is, the condition for the two-delay input control system has no zero is obtained for the systems in which geometric multiplicity of zeros of basic discrete-time system is greater than one. We investigate how to design an inverse system as an application of two-delay input control. It is shown that an asymptotic inverse system always exists, if two-delay input control system has no zeros. For a stable system, an inverse system is of finite inverse response. For an unstable system, the system is also designed using state feedback and observer. In particular, by choosing the feedback gain and observer gain suitably, we can obtain an inverse system in a finite time.

Conditions for Zero Avoidance of Two-delay Input Control Systems and Design of an Inverse System