Stability of thresholdbased sampling as metric problem
Autoren 
Bernhard Moser 
Editoren 

Titel  Stability of thresholdbased sampling as metric problem 
Buchtitel  Proceedings of the 1st IEEE International Conference on EventBased Control, Communication, and Signal Processing (EBCCSP 2015) 
Typ  in Konferenzband 
Verlag  IEEE 
ISBN  9781467378888 
DOI  DOI 10.1109/EBCCSP.2015.7300692 
Monat  June 
Jahr  2015 
Abstract  Thresholdbased sampling schemes such sendondelta, levelcrossing with hysteresis and integrateandfire are studied as nonlinear inputoutput systems that map Lipschitz continuous signals to event sequences with 1 and 1 entries. By arguing that stability requires an event sequence of alternating 1 and 1 entries to be close to the zerosequence w.r.t. the given event metric, it is shown that stability is a metric problem. By introducing the transcription operator T, which cancels subsequent events of alternating signs, a necessary criterion for stability is derived. This criterion states that a stable event metric preserves boundedness of an input signal w.r.t to the uniform norm. As a byproduct of its proof a fundamental inequality is deduced that relates the operator T with Hermann Weyl’s discrepancy norm and the uniform norm of the input signal. 