Question

The state transition matrix for the system $\dot{X}=AX$ with initial state $X\left(0\right)$ is

• A. $(sI-A{)}^{-1}$
• B. $e^{At}X\left(0\right)$
• C. Laplace inverse of $\left[\right(sI-A{)}^{-1}]$
• D. Laplace inverse of $\left[\right(sI-A{)}^{-1}X\left(0\right)]$

Answer 1

The correct option is C Laplace inverse of $\left[\right(sI-A{)}^{-1}]$

$e^{At}=L^{-1}[sI-A{]}^{-1}$