Repetitive process stability theory applied to the design of distributed controllers for spatially interconnected systems

Abstract

This paper considers differential linear repetitive processes that are a distinct class of two-dimensional continuous-discrete linear systems of both physical and systems theoretic interest. A well developed stability theory for these processes exists and this paper gives substantial new results on the use of this theory for controller design. The application area is distributed feedback controllers for spatially interconnected systems. In particular, the differential linear repetitive process setting is used to design controllers for spatially interconnected systems that are composed of several linear continuous-time subsystems, where each directly interacts with neighboring subsystems. This design is based on converting the problem to one of H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control for a differential linear repetitive process, leading to design based on linear matrix inequality computations. Specifically, sufficient conditions for the existence of a dynamic feedback controllers are developed together with the design algorithms for the associated controller matrices. A simulation based case study on the model of spring-mass system is given to demonstrate the feasibility and effectiveness of the new design.