Robust synthesis via bilinear matrix inequalities

Abstract

The μ/Km-synthesis formulation for robust controller synthesis with frequency dependent scalings/multipliers is shown to be equivalent to a bilinear matrix inequality (BMI) feasibility problem. Formulating the non-convex μ/Km-synthesis problem as a BMI problem allows local joint controller and multiplier synthesis using finite dimensional LMI-like optimization methods and also the application of global optimization techniques. The BMI approach improves on the standard D, G(SINGLE BOND)K-iteration, M(SINGLE BOND)K-iteration approaches to μ/Km-synthesis, and additionally allows controller order and structure constraints.