Decentralized fixed modes for LTI time-delay systems

This paper investigates the stabilization problem for a linear time-invariant (LTI) time-delay system by means of a decentralized finite-dimensional LTI output feedback controller. Both commensurate and incommensurate delays are considered. It is assumed that delay can appear in the state, inputs, and outputs of the system. In this case, using the definition of μ-decentralized fixed modes (μ-DFM) introduced in a recent work necessary and sufficient conditions for the decentralized stabilizability of LTI time-delay systems is obtained. Some algebraic conditions are also provided to determine if a mode of a time-delay system is a μ-DFM. A numerical algorithm is proposed to obtain the set of μ-DFMs of the system, and the notion of μ-approximate decentralized fixed modes (μ-ADFM) is also presented. Finally, three numerical examples are given to illustrate various applications of the results.