Topic: Control Systems
The matrix used for calculating the controllability is
- A. $[B~AB~A^{2}B...]$
- B. $[B~BA~BA^{2}...]$
- C. $[B~AB~2AB...]$
- D. $[B~-AB~-A^{2}B...]$
Answer: A. $[B~AB~A^{2}B...]$
Explanation: For a linear time-invariant system defined by $\dot{x} = Ax + Bu$, the controllability matrix $Q_c$ is defined as $Q_c = [B \quad AB \quad A^2B \dots A^{n-1}B]$. A system is fully controllable if this matrix has full rank $n$.