In the qualitative theory, the study of linear systems is very important, since a comprehensive analysis of nonlinear systems via perturbation techniques requires linear theory. This is due to the fact that in many cases, stability properties of solutions can be derived from the linearization along the solution, the so-called variational equation. In this chapter, methods are provided for the analysis of linear systems with respect to the notions of attractivity and repulsivity which have been introduced in Chapter 2.
KeywordsLinear System Null Space Invariant Projector Exponential Dichotomy Lyapunov Spectrum
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