On the Bilinear Matrix Inequality

M. Mesbahi, Jet Propulsion Laboratory

I present an overview of the some of key developments in the methodological, structural, and computational aspects of the Bilinear Matrix Inequality (BMI) problem. In this direction, I will discuss the importance of the BMI and its geometric properties, including interpretations of the BMI as a rank constrained Linear Matrix Inequality (LMI), as an Extreme Form Problem (EFP), and as a Semi-Definite Complementarity Problem (SDCP). I will conclude with sketching an outline for the future research on the BMI.