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The most general form of linear time-invariant time-delay systems described by delay-differential-algebraic equations is considered. Necessary and sufficient conditions for a mode of such a system to be delay-independent are derived. Then, such a system under centralised control is considered, and some necessary and sufficient conditions for a mode of such a system to be spectrally uncontrollable and/or spectrally unobservable independent of any time-delays are derived. Finally, such a system under a decentralised control structure is considered, and some necessary and sufficient conditions for a decentralised fixed mode to be independent of any time-delays are derived. An example to illustrate the use of the results is also presented.

Delay independence of modes, controllability, observability, and decentralised fixed modes