ESTONIAN ACADEMY
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eesti teaduste
akadeemia kirjastus
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SINCE 1952
 
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proceedings
of the estonian academy of sciences
ISSN 1736-7530 (Electronic)
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Removing the input derivatives in the generalized bilinear state equations; pp. 98–107
PDF | doi: 10.3176/proc.2009.2.02

Authors
Tanel Mullari, Ülle Kotta ORCID Icon, Palle Kotta, Maris Tõnso, Alan S. I. Zinober
Abstract

The paper suggests constraints on the coefficients ai, bi, cij of the bilinear continuous-time input-output model that yield generalized state equations with input derivative order lower than that in the input-output equations. In the limiting case when one removes the input derivatives altogether, these conditions provide a solution of the realizability problem. The new state coordinates are found step by step. We first find a coordinate transformation allowing the reduction of the maximal order of the input time derivatives by one and write the corresponding state equations. At the second step we find the next coordinate transformation to lower the maximal order of input time derivative in the new state equations, etc. At each step we check, what condition the coefficients should satisfy to make the next step possible.

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