Stability Study of Two Level Hierarchical Nonlinear Systems Plenary lecture

Linear system stability study leads generally to necessary and sufficient conditions and does not depend on the system representation. The task is different for nonlinear systems, for which only sufficient conditions are given, then their obtained stability domains depend on the choice of both the description of the studied system and the used stability method. To lead stability study, one can start with a suitable system description (resp. stability methods), then choose an adapted analysis method (resp. system description). Aggregation techniques based vector norms are used, in this paper, to stability study and the arrow form matrices, introduced by the author, for the description of the studied two level hierarchical systems. Then, non conservative stability and stabilisability conditions are formulated for the studied nonlinear systems and multimodel systems, and hybrid synchronisation conditions introduced for chaotic systems.