On February 24–26, 1999, the ﬁrst Workshop on Interval Applications to Systems
and Control with special emphasis on Modal Interval Analysis, MISC’99, was held
in Girona, Spain. 28 papers were presented at the workshop, covering the following
topics related to intervals: mathematical research, applications to computational
geometry, interval simulations, fuzzy systems, applications to robotics, stability
analysis and control systems design.
In this special issue, only a reduced selection of the papers presented at MISC’99
is included. Those who may be interested in the other presented papers, please ask
us for the proceedings volume.
The selected papers represent current research lines on intervals and some of
their applications, dealing with the main shortcomings of classical intervals: the
lack of fundamental algebraic properties and the computation of interval extensions
of continuous functions.
The ﬁrst paper corresponds to the tutorial keynote talk given by Professor Miguel
A. Sainz, University of Girona, Spain. The paper summarizes the most important
results and features of Modal Interval Analysis. The second paper, by S. Markov,
deals with the algebraic properties of interval vectors. In her paper, E. Popova
presents distributive relation on multiplication and addition of generalized proper
and improper intervals. The paper by S. Shary extends the interval Gauss-Seidel
method to the problems of outer estimation of generalized AE-solution sets to
interval linear systems. In the ﬁfth paper, P. Hertling uses twin arithmetic to compute
an underestimation for the range of a rational function over an interval. The last
paper by J. Armengol et al. is an application example of modal intervals to generate
error-bounded envelope trajectories.
We would like to thank all the participants of MISC’99 for their fruitful contri-
butions and the reviewers for their hard and thankless work.
ı and Miguel
Girona, May 2000