Upper bound for the norm of the inverse of a particular symmetric positive-definite matrix

Question

For a matrix $A$, by $||A||$, I mean the matrix-norm induced by the $\ell^2$-norm. Let $A\in\mathbb{R}^{m\times m}$, $B\in\mathbb{R}^{m\times p}$, $C\in\mathbb{R}^{n\times m}$, $D\in\mathbb{R}^{n\times p}$ with $||A|| < 1$. Define, $$ N_k := \begin{cases} CA^{k - 1}B, &\text{if }k \geq 1\\ D, &\text{if } k = 0\\ 0, &\text{otherwise}. \end{cases} $$ I need an upper bound for $\|(N_k^{\sf{T}}N_k)^{-1}\|$ in terms of the norms of the aforementioned matrices. Are there any useful results that may help me achieve this?