State stability
State stability is a term from control engineering . An initial stability always follows from a state of stability.
Types of vibrations
Basically, a distinction is made between stable, decaying and resonating vibrations (see figure), which correspond to those in mechanical physics, whereby the decaying vibrations are referred to as asymptotically stable and the resonating vibrations as unstable.
definition
The equilibrium state x g of a system is called stable (in the sense of Lyapunow ) or state- stable , if for every ε> 0 a number δ> 0 exists, so that at any initial state that the condition
- || x 0 || <δ
is fulfilled, the proper motion of the system fulfills the condition
- || x (t) || <ε , for t -> ∞
Fulfills.
Individual evidence
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