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Lyapunov's indirect method is an attractive method for analyzing stability ofnon-linear systems since only the stability of the corresponding linearizedsystem needs to be determined. Unfortunately, the proof for finite-dimensionalsystems does not generalize to infinite-dimensions. In this paper a unifiedapproach to Lyapunov's indirect method for infinite-dimensional system isdescribed. It is shown how existing sufficient conditions fit this frameworkand a new sufficient condition is presented.

Linearized stability analysis of nonlinear partial differential equations