Accessibility and System Reduction of Nonlinear Time-Delay Control Systems

This article addresses the problem of checking the accessibility property for nonlinear single-input-single-output retarded time-delay systems with constant commensurable delays, described by higher order input-output functional differential equations. Necessary and sufficient conditions are found to check the accessibility property, and sufficient conditions are found to decompose the system equations into accessible and non-accessible subsystems. The conditions are presented in terms of autonomous elements, i.e., functions that cannot be influenced by system input. The results are generalizations from the delay-free case. However, the proofs do not transfer to the time-delay case easily, since algebraic structures with different properties are used here.