Controllability

Controllability

1. Describes the ability of an external input to move the internal state of a system from any initial state to any other final state in a finite time interval

   • A state x0 is controllable at time t0 if for some finite time t1 there exists an input u(t) that transfers the state x(t) from x0 to the origin at time t1.

2. It is useful in order to determine if it's possible to chage a system's behaviour

   • This is done throught two important things to check
     • stabilization of an unstable system
     • Modificating the dinamics of the system

3. Considerations to determine controllability in an state space system

   • The controllability matrix must be full rank
     • This means that de determinant of the matrix must be diferent to zero.

4. Example

   • • Then the system is controlable
     • Rank 'c' equal to 3

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