Ore algebras: a polynomial approach to nonlinear time-delay systems

Abstract

In this paper Ore algebra defined over the field of meromorphic functions is introduced to provide a polynomial approach to nonlinear time-delay systems. In comparison to the systems without delays the polynomials related to the nonlinear time-delay systems belong now to the multivariate skew polynomial ring and have the sense of differential time-delay operators. Then the neccessary and sufficient condition for accessibility of nonlinear time-delay systems is presented in terms of common left factors of such polynomilas. The paper also introduces transfer functions of nonlinear time-delay systems and show their basic properties.