We propose state-feedback controller design methodologies using our recent results on uniform solvability of state-dependent matrix Lyapunov equations. The controller designs obtained do not involve recursive computations and have a simple form being essentially a linear feedback with state-dependent dynamic gains. Furthermore, the Lyapunov functions utilized in the designs are quadratic functions of the states. A static state-feedback controller using the weak Cascading Upper Diagonal Dominance (w-CUDD) concept is presented first. We then consider a dynamic state-feedback controller utilizing a dynamic high-gain scaling technique to obtain a controller under weaker assumptions. The designs obtained are applicable to a class of systems which is a generalization of the strict-feedback form as long as certain assumptions regarding relative magnitudes of terms that appear in the system dynamics are satisfied. The designed controllers provide global robust state-feedback asymptotic stabilization.