Structural properties of H ∞ discrete-time controllers based on J-lossless factorisations

The paper deals with a problem of numerically reliable synthesis of H∞-optimal discrete-time controllers based on J-lossless factorisations of the delta-domain chain-scattering models of continuous-time plants. Necessary and sufficient conditions for the existence of strictly proper H∞ discrete-time controllers are given. Both the regular problem concerning models with no zeros on the stability boundary and the extended problem of models with such zeros are discussed. It is shown that in the latter case some structural constraints always appear. Controllers are obtained via solving two coupled delta-domain algebraic Riccati equations.