Switched Differential Linear Repetitive Processes

Differential linear repetitive processes are a distinct class of 2D systems where information propagation in one of the two directions only occurs over a finite duration, termed the pass length. Information propagation in one direction of information propagation is governed by a linear differential equation, and in the second by a linear difference equation. Moreover, the output, or pass profile, produced on any pass acts as a forcing function on, and hence contributes to, the dynamics of the next one. The exact sequence of operation is that a pass is completed and then the process is reset to the original location for the start of the next one and so on, and the result can be oscillations that increase in amplitude in the pass-to-pass direction. In this paper, the general problem considered is where the along the pass dynamics switch at the end of each pass. In particular, stability tests are developed which extend to allow control law design for this property and can be computed using Linear Matrix Inequality (LMI) methods