The mathematical definition of observability:

In 1960 Rudolf E. Kálmán introduced a characterization he called observability to describe mathematical control systems. In control theory, observability is defined as a measure of how well the internal states of a system can be inferred from knowledge of its external outputs.

To Observe:

  • To notice someone doing something, or to notice something happening

  • To watch or study someone or something with care and attention in order to discover something

  • To watch it carefully with the hope of arriving at a judgment.