Algebraic and topological aspects of feedback stabilization
M. Vidyasagar, H. Schneider, Brian J. Francis · IEEE Transactions on Automatic Control · 1982
In this paper we give essentially complete results concerning various algebraic and topological aspects of feedback stabilization. In particular, we give necessary and sufficient conditions for a given transfer function matrix to have a right-coprime or a left-coprime factorization, and exhibit a large class of transfer function matrices that have both. We give the most general set of feedback stability criteria available to date, and derive a characterization of all compensators that stabilize a given plant. We give a definition of "proper" and "strictly proper" in an abstract setting and show that 1) ever strictly proper plant can be stabilized by a proper compensator, and 2) every compensator that stabilizes a strictly proper plant must be proper. We then define a topology for unstable plants and compensators, and show that it is the weakest topology in which feedback stability is a robust property.