Linearization and exponential stability

2014/04/14 by Hans Zwart, Zwart, Hans
Engineering · #Control and Stability of Dynamical Systems

paper · pdf · doi:10.48550/arxiv.1404.3475

Abstract

We give sufficient conditions such that the exponential stability of the linearization of a non-linear system implies that the non-linear system is (locally) exponentially stable. One of these conditions is that the non-linear system is Fréchet differential at the equilibrium, if it is only Gateaux differentiable, then we show by means of an example that the result does not hold.

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