Lie Algebras and Lie Groups in Control Theory

Abstract

The theory of differential equations and control have been linked very closely because most of the early applications of control theory were to engineering problems of the type which are most naturally described by ordinary differential equations. The questions of importance in control have helped to revitalize certain problem areas in differential equations and methods and tools from control have been useful in obtaining new results in differential equation theory. On the other hand, going back to the era of Lie himself, there has been close ties between Lie theory and differential equations. Thus it is not surprising that one finds that Lie theory and control are also closely connected. This "triangle" is the subject of this set of notes.