Lyapunov functionals and matrices for neutral type time delay systems

Abstract

In this chapter we present some basic results concerning the computation of quadratic functionals with prescribed time derivatives for linear neutral type time delay systems. The functionals are defined by special matrix valued functions. These functions are called Lyapunov matrices. Basic results with respect to the existence and uniqueness of the matrices are included. Some important applications of the functionals and matrices are pointed out. A brief historical survey ends the chapter. © 2012 Springer-Verlag GmbH Berlin Heidelberg.