The implementation of a controller, if not exact, may lead to the so-called fragility problem, i.e., the loss of expected closed-loop properties. In the present note, this difficult problem is dealt with considering robust static-output feedback (SOF) control for uncertain linear time-invariant systems. By analogy with robust analysis theory based on quadratic separation, a new formulation for the SOF design is shown to be a valuable way to tackle fragility issues. Indeed, the use of a quadratic separator for design purpose allows to define a whole resilient (nonfragile) set of SOF control laws. Results are formulated as matrix inequalities one of which is nonlinear. A numerical algorithm based on nonconvex optimization is provided ant its running is illustrated on classical examples from literature.