Nonconvex Polygon Interval Arithmetic as a Tool for the Analysis and Design of Robust Control Systems

This paper describes Nonconvex Polygon Interval Arithmetic (NPIA) and its implementation. NPIA is the arithmetic defined on the set of all polygons in the complex plane, and it is very useful to compute estimates of value sets of transfer functions including uncertain physical parameters in a reasonable computing time. If the transfer function can be written in such a way that each uncertain parameter appears at most once, then the estimate obtained is included in an ε neighborhood of the region enclosed by the outer boundary of the value set.