H2 and mixed H2/Hinf Stabilization and disturbance Attenuation for differential linear repetitive processes

Repetitive processes are a distinct class of two-dimensional systems (i.e., information propagation in two independent directions) of both systems theoretic and applications interest. A systems theory for them cannot be obtained by direct extension ofexisting techniques from standard (termed 1-D here) or, in manycases, two-dimensional (2-D) systems theory. Here, we give newresults towards the development of such a theory in H2 and mixedH2/Hinf settings. These results are for the sub-class of so-calleddifferential linear repetitive processes and focus on the fundamentalproblems of stabilization and disturbance attenuation.