Discussion of linear structured system and the disturbance rejection problem

Abstract

In this paper we present the structured linear system and revisit the exact disturbance rejection problem in a structural framework. Necessary and sufficient conditions are proposed for the solvability of the Disturbance Rejection by State Feedback (DRSF) problem and the Disturbance Rejection by Measurement Feedback (DRMF) problem. The associated system graph can be used to easily check whether or not the conditions hold. When the DRMF problem is not solvable, we investigate how many sensors are needed and where should they be located to make this problem solvable. Our analysis is performed in the context of structured systems which represent a large class of parameter dependent linear systems. This structured system gives us more understanding of the system.