A flexible structure model with collocated sensor/actuator pairs is considered. The resonant modes of the collocated structure are damped by designing a suitable Positive Position Feedback Controller (PPF). The control design frame work involves matching the eigen-structure of a desired reference system with that of the closed loop system. Matching of the eigen-structure reduces to solving a set of over determined linear equations in the controller parameters. If the linear equations do not have solution, then a least squares solution under stability constraints (both closed loop and controller stability) is computed. The stability constraints are found to be Linear Matrix Inequalities (LMIs) in the controller parameters; thus making the control design convex. Numerical examples illustrate the utility of the proposed control design. © 2021 American Automatic Control Council.