New results on strong practical stability and stabilization of discrete linear repetitive processes

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 control law design algorithms for the strong practical stability property. Relative to alternatives, the LMIs for stability have a simpler structure and it is not required to impose particular structures on the matrix variables. These properties are extended to control law design, including those where state vector access is not required. Illustrative numerical simulation examples conclude the paper.