Editing Sliding mode control (section)

===Theorem 2: Region of attraction===
For the system given by Equation&nbsp;({{EquationNote|1}}) and sliding surface given by Equation&nbsp;({{EquationNote|2}}), the subspace for which the <math>\{ \mathbf{x} \in \mathbb{R}^n : \sigma(\mathbf{x})=\mathbf{0} \}</math> surface is reachable is given by
:<math>\{ \mathbf{x} \in \mathbb{R}^n : \sigma^\intercal(\mathbf{x})\dot{\sigma}(\mathbf{x}) < 0 \}</math>
That is, when initial conditions come entirely from this space, the Lyapunov function candidate <math>V(\sigma)</math> is a [[Lyapunov function]] and <math>\mathbf{x}</math> trajectories are sure to move toward the sliding mode surface where <math>\sigma( \mathbf{x} ) = \mathbf{0}</math>. Moreover, if the reachability conditions from Theorem 1 are satisfied, the sliding mode will enter the region where <math>\dot{V}</math> is more strongly bounded away from zero in finite time. Hence, the sliding mode <math>\sigma = 0</math> will be attained in finite time.