Exponential stability

Summary

An equilibrium is exponentially stable when nearby solutions approach it at least as fast as a decaying exponential. It is a strong form of asymptotic stability that comes with an explicit rate. For a linear system $x' = Ax$, asymptotic and exponential stability coincide, and both mean that every eigenvalue of $A$ has negative real part. Exponential stability survives small perturbations of the system, which makes it the preferred notion in control theory. See the definition.