Delay-independent decentralized fixed modes for multi-channel LTI systems subject to input and output delays

This paper concerns stabilizability of a multi-channel linear time-invariant (LTI) system with delay in inputs and outputs by means of a finite-dimensional decentralized output feedback controller. This problem can be tackled by obtaining the set of unstable decentralized fixed modes (DFMs) of the system. Although the set of DFMs for LTI time-delay systems is generally delay-dependent, there exists a certain type of DFMs, which are delay-independent. In this work, the notion of delay-independent DFM (DIDFM) is defined, and algebraic conditions are provided under which a mode of a multi-channel LTI system subject to input and output delays is a DIDFM. The result of this paper is more general than that of [1], due to the fact that that all the modes of the system in [1] are assumed distinct.