Linear Systems and Linearization

  • Hal SmithEmail author
Part of the Texts in Applied Mathematics book series (TAM, volume 57)


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.


Characteristic Equation Implicit Function Theorem Characteristic Root Absolute Stability Positive Real Part 
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Copyright information

© Springer New York 2011

Authors and Affiliations

  1. 1.School of Mathematical and Statistical SciencesArizona State UniversityTempeUSA

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