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Stability and robustness of discrete linear repetitive processes in the finite frequency domain using the KYP lemma

This paper develops a new set of conditions for strong practical stability of linear discrete repetitive processes through use of the generalized version of the Kalman-Yakubovich-Popov Lemma, with an extension to examples with uncertainty. These new conditions reduce the problem of determining if an example has this stability property to checking for the existence of a solution to a set of linear matrix inequalities (LMIs) and, relative to alternatives, can reduce the level of conservatism. The validity of the developed results are demonstrated by numerical example. A numerical example is also given.