Application of interval analysis techniques to linear systems. I. Fundamental results

The authors establish results for continuous and rational interval functions which are of interest in their own right and which may find future applications. These results are used to study interval matrix exponential functions and to devise a method of constructing augmented partial sums which approximate interval exponential functions as closely as desired. The results are used to develop an algorithm. The authors demonstrate the applicability of their results by considering three specific examples: an RLC circuit; an instrument servomechanism; and the design of a minimum plant sensitivity optimal regulator