A frequency-partitioning approach to robust output control of uncertain discrete linear repetitive processes

Abstract

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 version of the Kaiman-YakubovichPopov (KYP) Lemma to develop new linear matrix inequality (LMI) based stability conditions and a control law design algorithm in the presence of polytopic uncertainty in the process model. The new algorithm results in a static output feedback control law that ensures robust stability along the pass and allows control requirements to be enforced over finite frequency ranges. Furthermore, a frequency-partitioning approach can lead to less conservative conditions for robust control. A numerical example to illustrate the application of the new design algorithm concludes the paper.