On Robust Disturbance Observer Design Using Semi-Definite Programming

This paper is concerned with optimal synthesis of disturbance observers guaranteeing closed loop robust tracking and disturbance rejection performance. The approach presented makes use of internal model-based estimation of exogenous disturbances, where the internal model dynamics is chosen with at least one of its eigenvalues at the origin. The synthesis is then formulated as an H_∞ weighted-sensitivity optimization for static output feedback (SOF) gain of a Luenberger observer. A linearization method is then implemented to solve the bilinear-matrix-inequality (BMI) constrained semi-definite program (SDP) for a (sub)optimal static gain.