ABSTRACT
In this chapter, various fundamental elements of the theory of linear time-varying systems are studied in both the continuous-time and discrete-time cases. The chapter is a revised and updated version of Chapter 25 that appeared in the first edition of The Control Handbook. The revision includes material on the existence of coordinate transformations that transform time-varying system matrices into diagonal forms, and the connection to the concept of “dynamic” eigenvalues and eigenvectors. Also included in the revision is the use of a simplified expression derived in [11] for the feedback gain in the design of a state feedback controller in the single-input case based on the control canonical form. Generalizations to the multi-input multi-output case can be carried out using the results in [12]. The theory begins in Section 3.2 after the following comments.
