Controllability

Controllability

1. Ability to induce any signal

2. Activating the signal on a given line

3. Concept introduced by Kalman

4. A system is controllable at time t0 if it can be transferred from any initial state x (t0) to any other state, by means of an unconstrained control vector, in a finite time interval

5. Definitions associated with the possibility of

   • Transfer from any initial state to any final state
   • Origin controllability
     • Transfer from any initial state to the origin
   • Reachability
     • Transfer the state from the origin to any final state

6. Controllable model

   • Controllability matrix is ​​full or maximum range

7. Non-controllable model

   • For some initial conditions there is no input capable of bringing the system to the origin

8. Model in state space

9. Determines if it is possible to control a system to modify its behavior, for example

   • Stabilization of an unstable system
   • Modification of the dynamics of the system