Robust impulse-to-peak synthesis: application to the control of an aerospace launcher

A robust synthesis problem via state-feedback involving impulse-to-peak performances is investigated. Even when considering models without uncertainty, the impulse-to-peak performance cannot be computed exactly and a somewhat conservative bound may be computed by LMI optimization. Our goal is first to tighten the bounds obtained in the previous reference using the quadratic stability framework when the state-space matrices are known to belong to a polytope of matrices. In a second stage, the robust state-feedback synthesis problem is tackled in the same setup for LTI discrete-time polytopic systems. These results are then applied to control the attitude of a space launcher during the atmospheric flight