LMIs - a Fundamental Tool in Analysis and Controller Design for Discrete Linear Repetitive Processes

Abstract

Discrete linear repetitive processes are a distinct class of 2D linear systems with applications in areas ranging from long-wall coal cutting through to iterative learning control schemes. The feature which makes them distinct from other classes of 2D linear systems is that information propagation in one of the two independent directions only occurs over a finite duration. This, in turn, means that a distinct systems theory must be developed for them. developed. In this paper, an LMI approach is used to produce highly significant results on the stability analysis of these processes and the design of control laws for them. These new results are, in the main, for processes with singular dynamics and for those with so-called dynamic boundary conditions. Unlike other classes of 2D linear systems, these control laws have a firm physical basis, and the LMI setting is also shown to provide a firm basis on which to characterize the robustness properties of these processes.

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ORCID for E Rogers: orcid.org/0000-0003-0179-9398

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