On the Smallest Enclosing Balls
Daizhan Cheng, Xiaoming Hu, Clyde F. Martin · Communications in Information and Systems · 2006
In the paper a theoretical analysis is given for the smallest ball that covers a finite number of points p 1 , p 2 , • • • , p N ∈ R n .Several fundamental properties of the smallest enclosing ball are described and proved.Particularly, it is proved that the k-circumscribing enclosing ball with smallest k is the smallest enclosing ball, which dramatically reduces a possible large number of computations in the higher dimensional case.General formulas are deduced for calculating circumscribing balls.The difficulty of the closed-form description is discussed.Finally, as an application, the problem of finding a common quadratic Lyapunov function for a set of stable matrices is considered.