Stabilization of Feedback Systems via Distribution of Delays

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Marcella M. Gomez and Richard M. Murray
2012 IFAC Workshop on Time Delay Systems

This paper investigates the results of distributing the delay of a single feedback system. To distribute the delayed feedback, the single delay is replaced by the sum of two distinct delays with the same effective delay. The statistical properties of the new distribution function in the feedback, namely the sum of two delta functions, are used to quantify the effectiveness of delay distribution. We show that the distribution is effective in reducing the magnitude of the open loop transfer function, thereby, decreasing the gain-crossover frequency and improving the phase margin. Finally, inspired by Orosz et al., we demonstrate an example of how these results can be used to design a controller using delays.