Linear Systems and Linearization

Abstract

Key to the analysis of nonlinear systems is determining the stability of the equilibria. The classical method of determining stability is to linearize the system about the equilibrium and to determine exponential rates of growth and decay for the associated linear system. The framework for carrying this out is taken up in this chapter. Although the method is similar to that for ODEs, the characteristic equation is more complicated, typically having infinitely many roots. Fortunately,all but finitely many of these roots have real part less than any given real number.