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A note on norm-based Lyapunov functions via contraction analysis (1308.0586v1)
Published 30 Jul 2013 in math.DS and cs.SY
Abstract: It is well know that for globally contractive autonomous systems, there exists a unique equilibrium and the distance to the equilibrium evaluated along any trajectory decreases exponentially with time. We show that, additionally, the magnitude of the velocity evaluated along any trajectory decreases exponentially, thus giving an alternative choice of Lyapunov function.