Section: New Results

Invariant sets for time-delay systems

Participants : Sorin Olaru [correspondent] , Mohammed Laraba [L2S] , Silviu Niculescu [L2S] .

The characterization of invaraint sets for dynamical systems affected by time-delays is a long standing research topic in our group and this year new results have been obtained [52] , [51] towards construction of invariant sets in the original state space (also called D-invariant sets) by exploiting the forward mappings. As novelties, the present paper contains a sufficient condition for the existence of ellipsoidal D-contractive sets for dDDEs, and a necessary and sufficient condition for the existence of D-invariant sets in relation to time-varying dDDE stability. Another contribution is the clarification of the relationship between convexity (convex hull operation) and D-invariance. In short, this shown that the convex hull of two D-invariant sets is not D-invariant but the convex hull of a non-convex D-invariant set is D-invariant.