Linear and numerical linear algebra in control theory: some research problems

AbstractThis paper presents an informal survey of theoretical and computational aspects of three linear-algebra problems arising in control theory, namely, the Sylvester-observer matrix equation, the matrix eigenvalue assignment problem, and the stability and stabilization of large second-order systems. Difficulties are highlighted. Recent developments are mentioned. Some research problems in these areas, which should be of interest to both linear algebraists and control theorists, are described