  Let us consider the following robust nonconvex quadratic optimization
problem: \begin{equation*} \begin{split} \min &~ \dfrac{1}{2} x^\top Ax+a^\top
x \\ \text{s.t.}~ & \alpha\leq\dfrac{1}{2}x^\top (B_1+\mu B_2)x+(b_1+\delta
b_2)^\top x \leq\beta,~ \forall~ \mu\in
[\mu_1,\mu_2],\forall~\delta\in[\delta_1,\delta_2], \end{split} \end{equation*}
where $A$, $B_1$, $B_2$ are real symmetric matrices,
$\mu_1,\mu_2,\delta_1,\delta_2,\alpha$, $\beta\in\mathbb{R}$ satisfying
$\mu_1\leq \mu_2$, $\delta_1\leq\delta_2$ and $\alpha<\beta$. We establish the
robust alternative result; the robust S-lemma and the robust optimality for the
above nonconvex problem.
