The regulation of the biomass specific growth rate is an important goal in many biotechnological applications. To achieve this goal in fed-batch processes, several control strategies have been developed employing a closed loop version of the exponential feeding law, an estimation of the controlled variable and some error feedback term. In the case of non-monotonic kinetics, the specified growth rate can be achieved at two different substrate concentration values. Because of the inherent unstable properties of the system in the decreasing portion of the kinetics function, stabilization becomes a crucial problem in this high-substrate operating region. In this context, the dynamic behavior of fed-batch processes with Haldane kinetics is further investigated. In particular, some conditions for global stability and performance improvement are derived. Then, a stabilizing control law based on a partial state feedback with gain dependent on the output error feedback and gain saturation is proposed. Although particular emphasis is put on the critical case of high-substrate operation, low-substrate regulation is also treated.