Common Zero Structure of Rational Matrix Functions

On the differential structure of matrix–valued rational inner functions

Rational Matrix Functions and Rank-1 Updates

Suppose f = p/q is a quotient of two polynomials and that p has degree rp and q has degree rq . Assume that f(A) and f(A+ uv ) are defined where A ∈ R, u ∈ R, and v ∈ R are given and set r = max{rp, rq}. We show how to compute f(A+uv ) in O(rn2) flops assuming that f(A) is available together with an appropriate factorization of the “denominator matrix” q(A). The central result can be interprete...

Design of a Fuzzy Controller Chip with New Structure, Supporting Rational-Powered Membership Functions

In this paper, a new structure possessing the advantages of low-power consumption, less hardware and high-speed is proposed for fuzzy controller. The maximum output delay for general fuzzy logic controllers (FLC) is about 86 ns corresponding to 11.63 MFLIPS (fuzzy logic inference per second) while this amount of the delay in the designed fuzzy controller becomes 52ns that corresponds to 19.23 M...

The Structure of Bivariate Rational Hypergeometric Functions

We describe the structure of all codimension-two lattice configurations A which admit a stable rational A-hypergeometric function, that is a rational function F all whose partial derivatives are non zero, and which is a solution of the A-hypergeometric system of partial differential equations defined by Gel’fand, Kapranov and Zelevinsky. We show, moreover, that all stable rational A-hypergeomet...

Dual Szegö pairs of sequences of rational matrix-valued functions

We study certain sequences of rational matrix-valued functions with poles outside the unit circle. These sequences are recursively constructed based on a sequence of complex numbers with norm less than one and a sequence of strictly contractive matrices. We present some basic facts on the rational matrix-valued functions belonging to such kind of sequences and we will see that the validity of s...