GATE EC 1997 Set 1 Q3.5 — Control Systems

A certain linear time invariant system has the state and the output equations given below

$$\begin{array}{c} {\left[\begin{array}{l} \dot{\mathrm{X}}_{1} \\ \dot{\mathrm{X}}_{2} \end{array}\right]=\left[\begin{array}{rr} 1 & -1 \\ 0 & 1 \end{array}\right]\left[\begin{array}{l} \mathrm{X}_{1} \\ \mathrm{X}_{2} \end{array}\right]+\left[\begin{array}{l} 0 \\ 1 \end{array}\right] u} \\ y=\left[\begin{array}{ll} 1 & 1 \end{array}\right]\left[\begin{array}{l} \mathrm{X}_{1} \\ \mathrm{X}_{2} \end{array}\right] \end{array}$$

If $X_{1}(0)=1, X_{2}(0)=-1, u(0)=0$, then $\left.\frac{d y}{d t}\right|_{t=0}$ is