Most control systems are contaminated with some level of time delay. Whether it appears due to the inherent system dynamics or because of the sensory feedback, the delay has to be resolved regarding the system stability. We explain an unprecedented and fundamental treatment of time delay in a general class of linear time invariant systems (LTI) following a strategy, which we call the ‘Direct Method’. The strengths of the method lie in recognizing two interesting and novel features, which are typical for this class of systems. These features enable a structured strategy to be formed for analyzing the stability of LTI-TDS (Time Delayed Systems). Vibration control settings are not immune from time delay effects. We present a case study on active control of vibration using linear full state feedback. We then apply the Direct Method on this structure to display the stability outlook along the axis of delay. There appears an interesting property, which is related to the determination of the imaginary (i.e. marginally stable) roots of LTI-TDS. We state a general lemma and proof on this point.

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