A problem that usually appears when putting a theoretical result into practice is the lack of operational homogeneity between the Real and the Digital lines. A digital number can have many digits, but in many cases it is only an approximation to a real one, so there is an error between the real number and the digital one. This error is propagated when it is used in a computer which implements finite precision floating-point arithmetic.

Moreover, very often the inputs of the problem include real parameters which are not known so they are measured. Experimental measurements give only approximations to the values of these parameters and hence the input data of the problem contains errors which also are propagated through the computations.

Therefore, the results of computations are digital numbers which are precise but inaccurate and, moreover, do not contain information about their accuracy. A way to increase the accuracy is decreasing the precision by using intervals. An interval is a range of numbers bounded by the interval's endpoints. It is imprecise but can be accurate. The width of an interval can be used to represent the error of an approximation. An interval represents all the values it contains, so a single pair of interval endpoints represents an infinite number of values, or a continuum.

Interval arithmetic is used to evaluate arithmetic expressions over sets of numbers contained in intervals. The result of any interval computation is a new interval. Interval arithmetic guarantees that the resulting interval of an interval computation contains the set of all possible resulting values, i.e. it is accurate. This is true even when interval arithmetic is implemented on a computer using finite precision floating-point arithmetic, provided that the operations are performed using appropriate rounding.

Thanks to these characteristics of intervals and interval arithmetic, interval computations open a wide variety of new opportunities in every field of science and technology, avoiding the risks which are intrinsic of finite precision floating-point arithmetic. Intervals allow to express the uncertainty in input data and to solve real problems obtaining validated solutions with guaranteed accuracy, thus connecting computing to the real world.

It has been shown that interval analysis is very powerful in efficiently bounding the range of a function and provides mathematically rigorous results. This capability is particularly welcome in robust control since a variety of analysis and design problems can be cast in the evaluation
of the range of functions over intervals. In the last years, several applications of interval analysis to robust identification, robust control, interval simulation and digital control under uncertainty have appeared in the literature.

Different tools and methods based on interval analysis have been developed to deal with these problems. These methods require interval computation as well as extensive symbolic-numeric computation.

This site intends to provide a convenient entry point into the world of interval methods and software for control. It provides links giving access to the up-to-date and most important information resources related to the topic: research projects that are underway, research groups and individuals who are active in the field, selected papers and software. It also provides the latest news about conferences, workshops, special issues and the like. Fulfilling this task is not possible, however, without the active participation of all of you who are interested in this topic too. Then only this site can become and stay truly relevant and helpful. We would like to invite any comments, news, suggestions, contributions and the rest. Thanks in advance.

Josep Vehí