The intensity and features of sensory stimuli are encoded in the activity of neurons in the cortex. In the visual and piriform cortices, the stimulus intensity re-scales the activity of the population without changing its selectivity for the stimulus features. The cortical representation of the stimulus is therefore intensity-invariant. This emergence of network invariant representations appears robust to local changes in synaptic strength induced by synaptic plasticity, even though: i) synaptic plasticity can potentiate or depress connections between neurons in a feature-dependent manner, and ii) in networks with balanced excitation and inhibition, synaptic plasticity determines the non-linear network behavior. In this study, we investigate the consistency of invariant representations with a variety of synaptic states in balanced networks. By using mean-field models and spiking network simulations, we show how the synaptic state controls the emergence of intensity-invariant or intensity-dependent selectivity by inducing changes in the network response to intensity. In particular, we demonstrate how facilitating synaptic states can sharpen the network selectivity while depressing states broaden it. We also show how power-law-type synapses permit the emergence of invariant network selectivity and how this plasticity can be generated by a mix of different plasticity rules. Our results explain how the physiology of individual synapses is linked to the emergence of invariant representations of sensory stimuli at the network level.