Abstract: The damping efficiency of a damper can be enhanced within an inertia system, however, excessive use of the damping enhancement mechanism of the inertia system may lead to overlarge the control force. Therefore, the damping enhancement degree of the inertia system should be properly controlled. The existing damping enhancement control method involves solving complex nonlinear equations, which makes them inconvenient for application. To control the damping enhancement of the inertia system more concisely and effectively, the closed-form design formulae of the inertia system are derived by the basis of the design principle of achieving the preset damping enhancement target. The closed-form expressions for the stochastic vibration responses and damping enhancement ratio of a single-degree-of-freedom (SDOF) structure with inertia system are derived by the grounds of the theory of random vibration. The closed-form optimal solutions of inertance-mass ratio, stiffness ratio, and nominal damping ratio for the inertia system are derived by considering the performance demands of seismic response mitigation, of the design guidance of targeted damping enhancement and of the damping enhancement principle. The derived formulae are used for the case design of a SDOF structure with the inertia system, and the results of abundant dynamic time-history analyses under multiple cases prove that the design formulae of the inertia system with targeted damping enhancement is correct, reliable and efficient. The design formulae can meet the performance demands and control the damping enhancement degree of the inertia system in the meanwhile. The design method for a multi-degree-of-freedom (MDOF) structure with inertia systems is proposed upon the closed-form formulae proposed and upon the master degree-of-freedom theory, and the validity of the method is verified by pertinent case design and analysis.