 
Summary: ROBUST STABILITY OF TIME DELAY
SYSTEMS: THEORY
John Chiasson # Chaouki Abdallah ##,1
# ECE Dept, University of Tennessee, Knoxville TN 37996,
USA, chiasson@utk.edu
## ECE Dept, University of New Mexico, Alburquerque NM
871311356, USA, chaouki@eece.unm.edu
Abstract: Given that a timedelay system is stable for some delay h 0 > 0, a
procedure is given to find the stability interval [h # 1 , h # 2 ] such that h 0 # [h # 1 , h # 2 ] and
for all h satisfying h # 1 < h < h # 2 the system is stable. Further, the system is shown
to be unstable if h = h # 1 or h = h # 2 . It is then shown how this can be applied to
test the robust stability (with respect to delay values) of a SmithPredictor based
controller.
Keywords: Time Delay, Stability, Smith Predictor
1. INTRODUCTION
This paper considers the robust stability of time
delay systems of the form
d n y
dt n
+
