This paper introduces a new robust controller with cascaded fuzzy blocks as a power system stabilizer (CFPSS) to enhance damping during low-frequency oscillations. This CFPSS is designed to act as a nonlinear lead-lag PSS with a given number of compensation blocks. To demonstrate the efficiency and the robustness of this proposed stabilizer, simulation results performed on the IEEE three-generator nine-bus multi-machine power system subjected to a three-phase short-circuit fault have been carried out. The parameters of the proposed PSS and those of the conventional IEEE linear lead-lag PSS have been tuned by a recently developed optimization technique (krill herd algorithm). The robustness of this novel CFPSS is proved, by optimizing the parameters of the two PSSs for one operating point (normally loaded system) and applying them to other operating points (case of heavy and low loads) with some key parameters variation. The obtained results have shown the superiority and the robustness of the CFPSS comparatively to the conventional IEEE lead-lag PSS in terms of oscillations damping over a wide range of operating conditions and against parametric variation. The same conclusions have been drawn in the case of a large power system (IEEE 16-machine, 68-bus test system) characterized by its local and inter-area oscillations modes.