How to formulate nonsingularity of matrix (I + A*B) in LMIs?

[Amir Hossein]

Consider I+A*B where A: (n*l) is a variable matrix and B: (l*n) is known. I am looking for some way to find a sufficient condition for nonsingularity of I+A*B

 

[micromass]

Let $\|~\|$ be any matrix norm. Then $\|A\|< \frac{1}{\|B\|}$ is a sufficient condition.

http://en.wikipedia.org/wiki/Matrix_norm
http://en.wikipedia.org/wiki/Neumann_series