Two types of studies for inverse systems (or inverse model) are developed by Silverman and by Sain. One is a type of studies to construct the inverse systems which make an identity transfer function matrix of tandem union with original system, the other is a type of studies to construct the inverse systems which make a transfer function matrix integral value of identified matrix. Both require differentiators to be realized. On the other hand, filtered inverse systems which are restricted pass band do not require differentiators. These inverse systems have been proposed by Yoshikawa using transfer function matrix and by Yamada using state space representation. In this paper, a design method of exact inverse model for a given model using norm criterion for differece between the model and plant is proposed. And applying this inverse model to Model Feedback Control System (MFCS), it was shown by the numerical simulations that the adverse effect of disturbances can be reduced and robust stability can be achieved.

In this paper, a design method of control systems which achieves disturbance rejection for the multiple-input systems using a dual observer is proposed. This method is extended our earlier work to more general case and has the following advantages.(1) An unobservable subspace of arbitrary dimension in the state space could be made by dual observer.In strictly multiple-input systems, poles of the unobservable subspace could be assigned arbitrarily. Therefore, according to the construction of the unobservable subspace using this method, the disturbance rejecting systems could be constructed. In this regards, the validity of constructed control system is shown by the numerical simulations for 3-mass spring system.

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An inverse system for a given time-invariant system has been used as a compensator. However, in control systems where traditional inverse system is applied, the adverse effects of sensor noise may give seriously influence to the systems because the inverse system generally has a characteristic of high gain in high frequency area. Therefore, in these control systems other compensators except the inverse system must be constructed with complex characteristics.

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