Low-frequency electromechanical oscillations is a topic of great concern in power system operation. Undamped oscillations reduce the power transfer capacity and can lead the system to blackouts. Since the 70s, synchronous generators operate with power system stabilizers that add damping torque to oscillations through the excitation system control. These controllers can have either a conventional fixed structure, composed by stages of gain and phase compensation, or a multi-band structure (MB-PSS), composed by three bands that correspond to a specific frequency range (low, intermediate and high frequency). In the MB-PSS structure, each band consists of two branches based on differential filters (with a gain stage and lead-lag blocks). This paper presents an approach based on the Newton-Raphson method for tuning MB-PSS for power systems taking into consideration several operating conditions to ensure robustness. The approach adjusts the controller's gains to place a set of poles into a region in the complex plane with a desired damping ratio. Firstly, the method is applied to the well-known single-machine infinite bus system represented by the Heffron-Phillips model. Secondly, an application to the multimachine South-Southeastern Brazilian power system is discussed considering different operating conditions. The convergence of the proposed approach is evaluated regarding the initial conditions, the desired damping ratio, and the set of monitored poles. Linear and nonlinear time-domain simulations validate the designed controllers. Finally, it is shown that the computational effort required by the proposed approach is lower than the one required by a class of methods widely reported in the literature for MB-PSS design. List of symbols and abbreviations: FACTS, flexible alternating current transmission systems; LFO, low-frequency oscillations; MB-PSS, multi-band power system stabilizer; PSS, power system stabilizer; PSS2B, stabilizer based on the integral acceleration power; PSS4B, multi-band power system stabilizer; STATCOM, static synchronous compensator; SVC, static Var compensator; Var, volt-ampere reactive; WADC, wide-area damping control; ΔU REF , reference voltage of the excitation system (pu); ΔU PSS , supplementary stabilizing signal (MB-PSS output) (pu); K a , gain of the excitation system (pu); R s , reactance of the stator (pu); T a , time constant of the excitation system; T 0 d0 , d-axis transient open circuit time constant of generator (s); X d , d-axis synchronous reactance of generator (pu); X 0 d , d-axis transient reactance of generator (pu); X q , q-axis synchronous reactance of generator (pu); f e , electric frequency (Hz); ξ d , desired damping ratio; ξ min , minimum damping ratio; ΔE FD , field voltage (exciter output) of generator (pu); ΔE 0 q , internal voltage of generator (pu); Δu, input variables vector; Δx, state variables vector; Δy, output variables vector; Δδ, internal angle of generator (rad); Δω pu , rotor speed deviation of generator (pu); ABCD, state, input, output, and feed-forwar...