LMI based stability analysis and controller design for a class of 2D discrete linear systems

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 distinct directions only occurs over a finite duration. In this paper we give an LMI based interpretation of stability for the sub-class of so-called discrete linear repetitive processes, both open loop and closed loop under a well defined practically relevant control law, and then apply this theory to solve currently open problems relating to robustness and stability margins for these processes. Also it is shown that the LMI approach to the computation of the stability margins for these processes can be combined with the recently developed concept of a pole for them to link these margins to expected performance - a key feature which is missing from the analysis of stability margins currently available in the 2D systems literature.