The Role of the 2D Lyapunov Equation in Stability and Control Law Design for 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 ID here) or (most often) 2D systems theory. In this paper, we continue the development of an applications oriented systems theory for the sub-class of so-called discrete linear repetitive processes which arise in both systems theoretic and applications studies. The new results relate to the use of a so-called 2D Lyapunov equation in both stability analysis and control law design