Residual generators for detecting failure in 2D systems

Dynamic redundancy relations of two-dimensional systems allow for an implementation of parity checks by means of two-dimensional dynamic models. The authors present a complete characterization of the admissible parity checks in the formal power series domain and provide a dynamic implementation which does not increase the intrinsic delays of the failure detection process. The parity checks are represented as elements of a free module over the ring of polynomials in two variables, whose structure is completely specified by a finite set of generators computed from the matrix fraction description of the system. Also presented is an explicit realization procedure of the polynomial matrix in two variables that constitutes the transfer matrix of the corresponding residual generator