In some practical problems, state derivative variables are more easily obtained than state variables. Solution of guaranteed cost control problem using derivative feedback for continuous, linear time-invariant systems in Reciprocal State Space form with or without polytopic uncertainties, is presented in this paper. Sufficient conditions on stability and performance are derived in terms of Linear Matrix Inequalities. State derivative and output derivative feedback gain matrices are found to minimise non-standard quadratic cost. Vibration attenuation performance of the proposed controllers are examined on an active suspension of a car seat example in the presence of suspension damping element failure. Numerical simulation results verify the superiority of guaranteed cost robust derivative feedback controllers over existing derivative feedback linear quadratic regulator controllers which are given in literature.