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RELATIVE ORDER OF SAMPLED LINEAR TIME-INVARIANT SYSTEMS

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The paper considers the rank behavior of the matrix leading coefficient of transfer function numerator of a sampled multidimensional linear time-invariant system when the sampling period tends to zero. Zero order hold sampling method is used. It is shown that the rank of the coefficient under consideration for all sufficiently small values of the sampling period is maximal if the natural condition of nonsingularity of the initial continuous prototype system is satisfied. In particular, if the dimensions of the system input and output coincide, then sampled system with a nonsingular leading coefficient is generated with any sufficiently small sampling period. This feature plays an important role in solving many problems of control theory. For example, the classical criterion of decouplability of linear systems requires the nonsingularity of the system interactor, and for systems with a nonsingular leading coefficient, this condition is satisfied automatically. In the following,while the synthesis of minimax regulators for general form discrete systems, the artificial reduction of the system to the form with the maximal rank of the leading coefficient is one of the first steps in an optimal regulator design.  The results of this work have proved that this step is superfluous if a discrete system under control is a result of sampling of a nonsingular system, as is often the case. The results of the work are illustrated by the example of an induction motor discrete model.

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