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A universal controller is designed for cascade systems, involving dynamic uncertainty, unknown nonlinearities, exogenous disturbances and/or time-varying parameters, capable of guaranteeing prescribed performance for the output tracking error, as well as uniformly bounded signals in the closed loop. By prescribed performance we mean that the output tracking error should converge to a predefined arbitrarily small residual set, with convergence rate no less than a certain prespecified value, exhibiting maximum overshoot less than a sufficiently small preassigned constant. The proposed control scheme is of low complexity, utilizes partial state feedback and requires reduced levels of a priori system knowledge. The results can be easily extended to systems affected by bounded state measurement errors, as well as to MIMO nonlinear systems in block triangular form. Simulations clarify and verify the approach.