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In this paper, we prove the genericity of the observability for discrete-time systems with more outputs than inputs. Mathematics Subject Classification. 57R40, 93B07, 93B27, 93C55. Let us recall the notion of observability investigated in this paper. Definition 1. Two initial conditions x 0 andx 0 and an input u = (u k ) k≥0 being given, x k andx k denote the points x k = f (x 0 , u k ) andx k = f (x 0 , u k ).doi:10.1051/cocv:2005001 fatcat:h4rgcfh6zrd2ngv7wgnxiozw5e