formalism and we show how it can be used in a general setting to define discrete time Floquet dynamics in the exclusion processes context. This method is valid for both periodic and open boundary conditions. We explain how the associated stationary state can be computed in a matrix product form. We illustrate the method with two examples: the Symmetric Simple Exclusion Process (SSEP) and the Asymmetric Simple Exclusion Process (ASEP). In section \[sec:generalized\_exclusion\] we use the method to introduce new integrable models with generalized exclusion rules where several particles are allowed on the same site. The building blocks of the models, the $R$ and $K$ matrices, are constructed through the fusion procedure. We present a precise description of the transition probabilities of the Markov matrix. The associated stationary state is exactly computed in a matrix product form, by introducing a new technique that we call *fused* matrix ansatz. We finally end up in section \[sec:conclusion\] with some concluding remarks and interesting open questions.

Integrable Floquet dynamics from transfer matrix formalism. \[sec:integrable\_Floquet\]
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Integrability and transfer matrix formalism.
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We give in this subsection a very brief review of integrability in the context of exclusion processes. We introduce the main objects 