OBSERVABILITY

OBSERVABILITY

1. Duality of controllability

2. Estimates the states of the system from the knowledge of their inputs and outputs

3. Supplementary structural characteristic of a state representation of a system

4. Use

   • Solve more quickly the problems of reconstruction of non-measurable state variables from those that yes are

5. Importance in practice

   • Control by state feedback
     • Some state variables are not accessible for direct measurement
       • It is necessary to determine the non-measurable variables to construct the control signals

6. A state xi is observable in t0 whenever it is possible to determine xi (t0) knowing y (t).

   • Given the system
     • it is observable if and only if the matrix O is of full rank (n)
       • Observability matrix

7. Non-observable states

   • Are those from which your output is permanently zero before null entry