Bilinearity and complementarity in robust control

We present an overview of the key developments in the methodological, structural, and computational aspects of the Bilinear Matrix Inequality (BMI) feasibility problem. In this direction, we present the connections of the BMI with robust control theory, 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). Computational implications and algorithms are also discussed.

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