About an Alternative S-Variable Condition for State-Feedback Design

The study of recent papers brought our attention to an alternative matrix inequality condition for state-feedback design. This condition falls in the category of S-variable results. At the difference of previous conditions it does not involve Schur complement or duality arguments and thus simplifies significantly the mathematical derivations. We provide in this paper a detailed description of the core elements of this new to us result. We then expose some derivations for pole location and time-response performances of uncertain systems with constant or time-varying uncertainties, as well as for some non-linear systems.