Control system synthesis via bilinear matrix inequalities

This paper introduces the bilinear matrix inequality (BMI) as a simple but flexible framework for approaching robust control system synthesis problems. The BMI is an extension of the linear matrix inequality (LMI) approach that has recently been found to be useful in formulating and solving a limited class of robust control problems, including state-feedback and full-order dynamical output feedback H^∞ control, μ/k_m analysis, simultaneous stabilization, gain-scheduling, and so forth. In particular, the BMI formulation is shown to offer the advantage of handling specifications not amenable to the LMI framework such as constraints on controller structure (e.g., decentralized "block-diagonal" control) and on controller order. The BMI formulation also sheds new insight into the properties and limitations of existing robust control algorithms such as the μ/k_m-synthesis, raising questions about the local optimality of the classical DK-iteration.