⏟ {u_{1} (mathbf x, z_{1}) = v_{1} + ̇ u_{x}}_{text B y d e f i n i t i o n o f v_{1}} = ⏞ {- \frac{\partial V_{x}}{\partial mathbf x} g_{x} (mathbf x) - k_{1} (⏟ {z_{1} - u_{x} (mathbf x)}_{e_{1}})}^{v_{1}} + ⏞ {\frac{\partial u_{x}}{\partial mathbf x} (⏟ {f_{x} (mathbf x) + g_{x} (mathbf x) z_{1}}_{̇ mathbf x text (i . e ., \frac{operatorname d mathbf x}{operatorname d t} text)})}^{̇ u_{x} text (i . e ., \frac{operatorname d u_{x}}{operatorname d t} text)}