Output feedback control of discrete linear repetitive processes over finite frequency ranges

Discrete linear repetitive processes operate over a subset of the upper-right quadrant of the 2D plane. They arise in the modeling of physical processes and also the existing systems theory for them can be used to effect in solving control problems for other classes of systems, including iterative learning control design. This paper uses a form of the generalized Kalman-Yakubovich-Popov (GKYP) Lemma to develop new linear matrix inequality (LMI) based stability conditions and an output control law design algorithm. The new algorithm results in a static output feedback control law that ensures stability along the pass and meets the control requirements in finite frequency ranges. Relative to alternatives, the new results in this paper reduce the conservatism in existing designs and should easily extend to design in the presence of uncertainty in the process model. A numerical example to illustrate the application of the new design algorithm concludes the paper.