# tracking error state space, linear control example

I am trying to understand a detail from an example, from the control textbook Slotine and Li (1991) "Applied Nonlinear Control", Prentice-Hall, Example 6.4, pag. 220. A linear system is given:

\eqalign{ \left[ {\matrix{ {{{\dot x}_1}} \cr {{{\dot x}_2}} \cr } } \right] =& \left[ {\matrix{ {{x_2} + u} \cr u \cr } } \right] \cr\\ y =& {x_1} \cr}

where the output $y$ is desired to track $y_d$. Differentiating the output, an explicit relation between $y$ -output- and $u$ -control input- is obtained:

$$\dot y = {x_2} + u$$

Until here it is clear. Now, the authors choose a control law:

$$u = - {x_2} + {{\dot y}_d} - (y - {y_d})$$

and say that this yield the tracking error equation:

$$\dot e - e = 0$$

with the $e$ being the tracking error, defined as $e=y-y_d$ and the internal dynamics: $${{\dot x}_2} + x = {y_d} - e$$ ... and the problem continues.

My question is: how does one define the control law $u = - {x_2} + {{\dot y}_d} - (y - {y_d})$ ?? And how does this relate to the two following equations ($\dot e - e = 0$ and ${{\dot x}_2} + x = {y_d} - e$)?

Any clarifying answer is much appreciated.

Thanks