On families of systems and deformations

Until recently, there has not been any systematic effort towards a theory of systems with parameter variations. It is presently suggested that the concept of families of systems is basic to such an effort, and entails the techniques of Lie theory, differential geometry, and algebraic geometry. Attention is given to the geometric characterization of certain families of systems that appear in control and identification problems. The ways in which families of systems degenerate as parameter variations become large are isolated, using the topological rather than algebraic geometric case.