Section: New Results

Left invertibility and its applications

Participants : Jean-Pierre Barbot, Thierry Floquet, Gang Zheng, Lei Yu.

For secure communication based on chaos, we introduced a new class of chaotic hybrid delayed systems, which is at our opinion a real improvement with respect to the known plain text attack [67] . In the same way our theoretical improvement with respect to the left invertibility problem [21] has a great potential application in diagnostic, secure communication and identification. Moreover, we gave a new method to classify the way to chaos with respect to non smooth bifurcation [16] and some other preliminary results were given at the 2nd IFAC Chaos conferences [39] . Since normal form [17] can be used to analyze and classify systems with respect to control theory properties, we have used for the first time such normal form for studying whether a system is flat or not [40] . Some applications in power electronic [51] and Tire/road identification [65] were realized.