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This paper deals with stochastic model predictive control of constrained discrete-time periodic linear systems. Control inputs are subject to periodically time-varying polytopic constraints with possibly time-dependent state and input dimensions. A stochastic constraint is instead enforced on the system state process imposing a bound on the average over time of state constraint violations. Disturbances are additive, bounded and described by a periodically time-dependent probabilistic distribution. The aim of this paper is to develop a receding horizon control scheme which enforces recursive feasibility for the closed-loop state process. The effectiveness of the proposed algorithm is finally shown through a simulation study on a building climate control case.