In this paper we develop a fixed-architecture controller analysis and synthesis framework that addresses the problem of multivariable linear time-invariant systems subject to plant input and plant output time-varying nonlinearities while accounting for robust stability and robust performance over the allowable class of nonlinearities. The proposed framework is based on the classical Lure´problem and the related Aizerman conjecture concerning the stability of a feedback loop involving a sector-bounded nonlinearity. Specifically, we extend the classical notions of absolute stability theory to guarantee closed-loop stability of multivariable systems in the presence of input nonlinearities. In order to capture closed-loop system performance we also consider the minimization of a quadratic performance criterion over the allowable class of input nonlinearities. Our approach is directly applicable to systems with saturating actuators and provides full and reduced-order dynamic compensators with a guaranteed domain of attraction. The principal result is a set of constructive sufficient conditions for absolute stabilization characterized via a coupled system of algebraic Riccati and Lyapunov equations. The effectiveness of design approach is illustrated by several numerical examples.