Stability margins of continuous-discrete 2D linear systems and their application to the design of iterative learning control laws for differential systems

This paper considers the class of 2D linear systems where a linear differential equation governs information propagation in one of the two directions, and in the other, the updating is governed by a difference equation; in some of the literature, these systems are referred to as mixed or hybrid. Linear repetitive processes are a particular case of such systems that have been used in several areas, such as iterative learning control. Stability margins for these systems have received attention in the literature. In this paper, new results on these margins for differential linear repetitive processes are derived and applied to iterative learning control law design. Sufficient conditions for computing the required stability margins are formulated using linear matrix inequalities, which can be readily adapted to design the required controllers. Finally, the applications of the developed results to design of ILC scheme for a typical actuator in a tracking servo system is presented to demonstrate the effectiveness of the design and highlight its advantages over existing alternatives.