diff --git a/docs/Chapters/1-MODERN-CONTROL.md b/docs/Chapters/1-MODERN-CONTROL.md index 61fe745..4050b02 100644 --- a/docs/Chapters/1-MODERN-CONTROL.md +++ b/docs/Chapters/1-MODERN-CONTROL.md @@ -107,21 +107,24 @@ $$ > > Then, put all variables equal to the previous one derivated: > -> $x(t) = \begin{bmatrix} -> x_1(t)\\ -> x_2(t) = \dot{x_1}(t)\\ -> \dots\\ -> x_n(t) = \dot{x}_{n-1}(t) -> \end{bmatrix} -> \; -> \dot{x}(t) = \begin{bmatrix} -> \dot{x_1}(t) = x_2(t)\\ -> \dot{x_2}(t) = x_3(t)\\ -> \dots\\ -> \dot{x}_{n-1}(t) = \dot{x}_{n}(t)\\ -> \dot{x}_{n}(t) = \text{our formula} -> \end{bmatrix}$ -> +$$ +x(t) = \begin{bmatrix} + x_1(t)\\ + x_2(t) = \dot{x_1}(t)\\ + \dots\\ + x_n(t) = \dot{x}_{n-1}(t) + \end{bmatrix} +\; +\dot{x}(t) = \begin{bmatrix} + \dot{x_1}(t) = x_2(t)\\ + \dot{x_2}(t) = x_3(t)\\ + \dots\\ + \dot{x}_{n-1}(t) = \dot{x}_{n}(t)\\ + \dot{x}_{n}(t) = \text{our formula} + \end{bmatrix} + +$$ + Now in our state we may express `position` and `speed`, while in our `next_state` we'll have `speed` and `acceleration`: