Closed - Form Expressions of Convex Com - binations with Application in Control

Convex combinations are used to express a point in a set as a weighted sum of the extreme points of this set. Therefore, convex combinations are used in many different applications, including control. When controlling linear parameter varying systems which are affected by disturbances, there exist robust control algorithms [1] which use convex combinations to interpolate between extreme controllers depending on the current disturbance. These controllers are used for example for space shuttles which are affected by wind and electromagnetic interferences, but also helicopters, wind power plants, and robotic manipulators, etc.