An LMI approach to positivity embedding

Positivity-based control design provides closed-loop stability regardless of parametric variations and unmodeled dynamics. However, the colocation design, often required for ensuring positive real plant, is excessively conservative. Recently dynamic embeddings have been introduced to reduce conservativeness by allowing also noncolocated and nonsquare plants. The technique used to compute these dynamic embeddings requires solving an involved convex optimisation problem with accompanying slow convergence. This paper introduces an improved method by formulating the dynamic embedding problem in a linear matrix inequality (LMI) format taking advantage of a recently available algorithm in solving the LMI efficiently. A numerical example using the Draper Tetrahedral Truss demonstrates the improvement in efficiency and accuracy over the previous method in computing dynamic embeddings