Definition
The term stability as used in this entry is a property of an equilibrium of a dynamic system. There are various definitions of stability which describe how a dynamic system being at an equilibrium reacts on a small disturbance (Plaschko and Brod 1995). In machining science, the Lyapunov stability and the asymptotic stability are of high interest. Consider the continuous dynamic system:
We suppose that the system has an equilibrium at
Lyapunov Stability
The above equilibrium is called Lyapunov stable, if
such that
This means that solutions starting within a range of δ from the equilibrium will forever stay within a range of ϵ to the equilibrium.
Asymptotic Stability
An equilibrium is called asymptotically...
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Biermann, D., Surmann, T. (2019). Stability. In: Chatti, S., Laperrière, L., Reinhart, G., Tolio, T. (eds) CIRP Encyclopedia of Production Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53120-4_6542
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