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This paper solves the robust hybrid output regulation problem for arbitraryuncertain hybrid MIMO linear systems with periodic jumps without therestrictive assumptions used in all previous works on the subject. A necessarycondition for solving the problem is that the regulator must incorporate aninternal model of the flow zero-dynamics, which is typically affected byuncertainties and then unknown. Hence, the proposed regulator consists of threeunits: a data-driven estimator of the dynamics that are invisible from theregulated output during flows, a flow internal model in charge of achievingregulation during flows, and a jump internal model in charge of imposing asuitable reset of the state at each jump.

Robust Hybrid Output Regulation for Linear Systems with Periodic Jumps: the non-semiclassical case