Quantized state systems method: Difference between revisions

Revision as of 11:52, 6 July 2015

Revision as of 22:35, 6 July 2015

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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>.