Matrix Theory and Control
Peter Lancaster, Leiba Rodman · 1995
Abstract The ideas and theory presented in this chapter will play important parts in our study of Riccati equations. They revolve around the concepts of controllable (and observable) matrix pairs. The importance of these concepts was recognized in the early years of development of control theory and it was in that context that the terms “controllable” and “observable” arose and have some physical meaning. Our approach uses linear algebra in the development of these concepts because it is this understanding that is required in the sequel. Their significance in the context of systems theory and control is mentioned as the chapter progresses, but is not given complete mathematical development.