Pole assignment in vibrating systems with time delay: An approach embedding an a-priori stability condition based on Linear Matrix Inequality

•A new idea for the pole placement in linear vibrating systems with time delay is proposed.•An a-priori stability condition is embedded in the controller synthesis.•Linear Matrix Inequality is adopted to formulate the stability condition for a bounded time delay.•A two-stage approach is proposed.•Receptances are adopted in the first stage; the first-order formulation is adopted in the second one.