System Verification by Regional Mobius Transformation

摘要

In this paper, we discuss the region transformation in safety verification problem: how to choose the region transformation of the system equation so that the newly obtained system is safe in a given initial region and a unsafe region, and the variable substitution is conformal and reversible. Firstly, conformal mapping theory in complex analysis is used to construct conformal transformation that maps the interior of the initial region to the exterior of the unsafe region. Then, by transforming the differential equation system, a region transformation method is proposed to construct the system under the coordinate transformation. An example is given to illustrate our idea.