Editing Lyapunov stability (section)

==Stability for systems with inputs==

A system with inputs (or controls) has the form

:<math>\dot{\textbf{x}} = \textbf{f}(\textbf{x}, \textbf{u})</math>

where the (generally time-dependent) input u(t) may be viewed as a ''control'', ''external input'',
''stimulus'', ''disturbance'', or ''forcing function''.  It has been shown <ref>Malkin I.G. Theory of Stability of Motion, Moscow 1952 (Gostekhizdat) Chap II para 4 (Russian) Engl. transl, Language Service Bureau, Washington AEC -tr-3352; originally On stability under constantly acting disturbances Prikl Mat 1944, vol. 8 no.3 241-245 (Russian); Amer. Math. Soc. transl. no. 8</ref> that near to a point of equilibrium which is Lyapunov stable the system remains stable under small disturbances.  For larger input disturbances the study of such systems is the subject of [[control theory]] and applied in [[control engineering]].  For systems with inputs, one must quantify the effect of inputs on the stability of the system.  The main two approaches to this analysis are [[BIBO stability]] (for [[linear system]]s) and [[input-to-state stability]] (ISS) (for [[nonlinear system]]s)