Stable Decoupling of Linear Time-Delay Systems Using Static-State Feedback

Abstract

This article presents a solution to the problem of stable decoupling, also known as noninteractive control, for continuous-time, linear time-delay systems using static state feedback. The system may involve both commensurate and non-commensurate pure delays, of both retarded and neutral types, as well as distributed delays. Such a system can be viewed as one over a ring, particularly an integral domain, which is not a unique factorization domain. The relevant algebraic properties of this ring are examined. We assume that the system to be decoupled is reachable and has an equal number of inputs and outputs. Since pre-stabilization does not compromise stable decoupling, we may assume that the system is stable. A stability-preserving and decoupling static-state feedback is then designed, with coefficients taken from the same ring as those of the system. Decoupling simplifies the subsequent control design while allowing for a partial spectrum assignment.