I need the following inequality to hold;
$$ M+(CK)^{\text{T}}NCK > 0 $$
where
$$ C \in \mathbb{R}^{m \times p}, ~~~ N=N^{\text{T}} > 0 \in \mathbb{R}^{m \times m} $$
are known, and
$$ M=M^{\text{T}} \in \mathbb{R}^{n \times n}, ~~~ K \in \mathbb{R}^{p \times n} $$
are unknowns which need to be solved for.
My attempt:
My initial thought is to use Schur's compliment to convert the inequality into an LMI in $M$ and $K$. Note that $N$ is invertible by definition. Thus, it follows that the inequality can be written as.
$$ M+(CK)^{\text{T}}NN^{-1}NCK > 0 $$
The problem is the sign of the second term on the left side of the inequality. Attempting to overcome this, I wrote the following;
$$ M-(-(CK)^{\text{T}}NN^{-1}NCK) > 0 $$
which is equivalent to $$ M-i(CK)^{\text{T}}NN^{-1}NCKi > 0 $$
where $ i=\sqrt{-1}$
Then, using Schur's compliment I wrote
$$ \begin{bmatrix} M & i(NCK)^{\text{T}} \\ iNCK & N \end{bmatrix} > 0 $$
I then attempted to use MATLAB to solve the LMI; however, feasp does not allow for imaginary numbers.
I am stuck and Have been unable to come up with any manipulations that would help me to solve this problem. Any suggestions on how I can convert $$ M+(CK)^{\text{T}}NCK > 0 $$ into an LMI in $M$ and $K$?