Finite frequency domain design of dynamic controllers for differential linear repetitive processes

Repetitive processes make a series of sweeps, or passes, through dynamics defined over a finite duration. One application area is iterative learning control where the stability theory for these processes can be used for design but this involves frequency attenuation over the complete frequency spectrum. This paper develops a new set of conditions where the stability property is only enforced over a finite frequency range. These conditions are developed using the generalized Kalman-Yakubovich-Popov lemma and can be implemented as a set of linear matrix inequalities. An extension to enable stabilizing control law design with additional applications relevant performance specifications, if required, is also developed.