Hierarchical Control of Linear Systems from the Abstraction Feedback Gain

Abstract

In this paper, the problem of hierarchical control for a class of linear systems is addressed. Given a large-scale linear system, we obtain a stabilizing feedback gain for it from that of an abstract system. And then, we employ this feedback gain to design a new interface between the original system and the abstraction. Furthermore, the synthesis of the new interface can be allowed by a new simulation function characterized by a low-order matrix associated to the abstraction. Finally, an example is given to illustrate the proposed approach.