Content deleted Content added
mNo edit summary |
No edit summary |
||
Line 14:
:<math> \dot{x}(t) = f(q(t), t), \quad x(t_0) = x_0. </math>
where <math>x</math> and <math>q</math> are related by a ''[[Hysteresis|hysteretic]] quantization function''
<math>q(t) = \begin{cases}x(t) && \text{if } \left|x(t) - q(t)\right| \geq \Delta Q \\ q(t^{-}) && \text{otherwise}\end{cases}</math>
where <math>\Delta Q</math> is called a ''quantum''. Notice that this quantization function is '''hysteretic''' because it has ''memory'': not only is its output a function of the current state <math>x(t)</math>, but it also depends on its old value, <math>q(t^{-})</math>.
This formulation therefore approximates the state by a piecewise constant function, <math>q(t)</math>, that updates its value as soon as the state deviates from this approximation by one quantum.
| |||