Control of a class of wave discrete linear repetitive processes

Repetitive processes are a distinct class of two-dimensional (2D) systems (i.e. information propagation in two independent directions occurs) of both systems theoretic and applications interest. They cannot be controlled by direct extension of existing techniques from either standard (termed 1D here) or (most often) 2D systems theory. In this paper we define a new model for these processes necessary to represent dynamics which arise in some applications areas and which are not included in the currently used models. Then we proceed to define quadratic stability for this case, obtain conditions for its existence, and also solve the problem of designing a control law to stabilize the process dynamics (including the case when there is uncertainty associated with the defining state space model).

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