Zero crossings, overshoot and initial undershoot in the step and impulse responses of linear systems

Titelangaben

Damm, Tobias ; Muhirwa, Luc N.:
Zero crossings, overshoot and initial undershoot in the step and impulse responses of linear systems.
In: IEEE Transactions on Automatic Control. Bd. 59 (2014) Heft 7 . - S. 1925-1929.
ISSN 1558-2523
DOI: https://doi.org/10.1109/TAC.2013.2294616

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Abstract

We consider functions in the time and the frequency domain, and show how the occurrence of real zeros in the frequency domain is related to the number of zero crossings, overshoot and initial undershoot in the time domain. This leads to simple proofs of known facts for linear time-invariant systems and their generalizations in various directions. In particular, we consider time-delay systems and differential systems of fractional order.