Interval Analysis

Abstract

This chapter presents reachability analysis methods to over-approximate reachable sets by intervals using classical notions from the field of interval analysis. Unlike other reachability analysis methods presented in later chapters, which rely on mathematical properties satisfied by the system for the computation of these over-approximations, interval analysis is a more straightforward approach where state and input variables bounded in intervals are propagated through the system dynamics to obtain an interval over-approximation of the reachable set. This propagation is obtained by extending the definitions of the four arithmetic operators (addition, subtraction, multiplication, division) to be applicable to interval variables, or more generally to interval matrices.