Target set and target tube reachability criteria for approximated discrete systems

S is taken to be a discrete linear dynamical system. The matrices A(k+1,k), B(k+1,k) and C(k+1) describing S are assumed to be unknown. M is a linear model of S described by known matrices Am(k+1,k), Bm(k+1,k) and Cm(k+1). The dimension of A is permitted to exceed Am. A known error bound ?? describes the approximation of S by M, i.e., it is assumed that a bound is available on the error between the outputs of M and S corresponding to the same input. A target set Yt is said to be strongly reachable from S (at time k) if a control sequence can be found such that the output of S remains within Yt from time k until the terminal time N. Using the theory of convex analysis, necessary and sufficient conditions are described for strong reachability of Yt. The target set reachability problem for deterministic systems (?? = 0) and norm uncertain systems (?? depends linearly on the norm of control) are considered as special cases of the main result.