Editing Exponential stability (section)

{{Short description|Continuous-time linear system with only negative real parts}}

{{Differential equations}}

In [[control theory]], a continuous [[LTI system theory|linear time-invariant system]] (LTI) is '''exponentially stable''' if and only if the system has [[eigenvalue]]s (i.e., the [[pole (complex analysis)|pole]]s of input-to-output systems) with strictly negative real parts (i.e., in the left half of the [[complex plane]]).<ref>David N. Cheban (2004), ''Global Attractors Of Non-autonomous Dissipative Dynamical Systems''. p.&nbsp;47</ref> A discrete-time input-to-output LTI system is exponentially stable if and only if the poles of its [[transfer function]] lie strictly within the [[unit circle]] centered on the origin of the complex plane. Systems that are not LTI are exponentially stable if their convergence is [[bounded function|bounded]] by [[exponential decay]].
Exponential stability is a form of [[asymptotic stability]], valid for more general [[dynamical systems]].