Controllability's dependence on B matrix

1. Is controllability same as reachability?
2. How do you know if a system is controllable?
3. What is controllability matrix?

Is controllability same as reachability?

The reachability property of the system means an existence of a control signal, which transposes the system from zero initial state to any designed final state. The controllability of the system means an existence of a control signal, which transposes the system from any initial state to final zero state.

How do you know if a system is controllable?

A system is controllable or "Controllable to the origin" when any state x₁ can be driven to the zero state x = 0 in a finite number of steps. If the second equation is not satisfied, the system is not .

What is controllability matrix?

The Controllability Matrix is defined as. — recall that A is n×n and B is n×1, so C(A,B) is. n×n; — the controllability matrix only involves A. and B, not C. We say that the above system is controllable if.