State-dependent computation is one of the main signatures of cognition. Recently, it has been shown how it can be used as a computational primitive in spiking neural networks for constructing complex cognitive behaviors in neuromorphic agents. However, to achieve the desired computations and behaviors in mixed signal analog-digital neuromorphic electronic systems, these computational primitives should be able to cope with noisy and imprecise components, such as silicon neurons and synapses, with noisy and unreliable external signals, and with interference from the environment. Here we present a spiking neural network model that addresses all these issues while exhibiting both analog signal processing properties and digital symbolic computational abilities. We show how this Neural State Machine (NSM) model can be used for realizing robust state-dependent computation on neuromorphic hardware, and we validate it with experimental results obtained from a recently developed multi-neuron multi-core neuromorphic computing architecture.