The paper deals with a problem of numerically reliable synthesis of H_(infinity)-optimal discrete-time observers based on dual J-lossless factorisations of delta-domain models of estimated processes. Both the regular problem concerning models with no zeros on the stability boundary and the extended problem of models with such zeros are discussed. Solutions are obtained via solving a delta-domain algebraic Riccati equation and a relative condition number of this equation is used as a measure of its numerical conditioning. An example is given to show that solutions obtained for the delta operator are much better conditioned than its counterpart versions based on the common forward shift operator.
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