LMI based stability analysis and robust 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 main 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. In this paper, the major new development is that an LMI based reformulation of the stability conditions can used to enable the design of a family of control laws which have a well defined physical basis. It is also noted that this setting can be used to investigate robustness aspects. Copyright © 2003 John Wiley & Sons, Ltd.