- ▪W. Dicks, E.D. Sontag, "Sylvester domains", J. Pure Appl. Algebra, vol. 13, no. 3, pp. 243–275, 1978. pdf
Abstract
The inner rank of an m x n matrix A over a ring is defined as the least integer r such that A can be expressed as the product of an m x r and an r x n matrix. For example, over a (skew) field this concept coincides with the usual notion of rank. This notion is studied in this paper, and is related to Sylvester's law of nullity and work by P.M. Cohn.
- ▪E.D. Sontag, "On split realizations of response maps over rings", Information and Control, vol. 37, no. 1, pp. 23–33, 1978. pdf
Abstract
This paper deals with observability properties of realizations of linear response maps defined over commutative rings. A characterization is given for those maps which admit realizations which are simultaneously reachable and observable in a strong sense. Applications are given to delay-differential systems.
- ▪E.D. Sontag, "On first-order equations for multidimensional filters", IEEE Trans.\ Acoustics, Speech, and Signal Processing, vol. 26, pp. 480–482, 1978. pdf
Abstract
A construction is given to obtain first-order equation representations of a multidimensional filter, whose dimension is of the order of the degree of the transfer function.
- ▪E.D. Sontag, "Algebraic-geometric methods in the realization of discrete-time systems", In Proc.\ Conf.\ Inform.\ Sci.\ and Systems, John Hopkins Univ. (1978), pp. 158–162, 1978.