Determining the Viability of an Unbounded Polyhedron for a Switched System

This paper proposes a new method to determine the viability of switched system on cone and an unbounded polyhedron. First, we investigate condition cone. Then, sufficient criterion for polyhedron, which is expressed by convex hull finite number extreme points nonnegative linear combination directions, presented using nonsmooth analysis. Based this criterion, instead all boundary points, just several directions are needed be verified whether satisfying some conditions. The advantage proposed methods that determining easy implemented. Finally, example listed illustrate effectiveness methods.