The work in the framework of the project ANR ArHyCo is organized in three tasks.

• Task 1: Switched systems with periodic steady state
  Responsible : Mario Sigalotti (INRIA - IECN)
  
  This task aims at understanding some fundamental hybrid systems properties and provide analysis and design tools that modern applications demand. Hybrid systems with periodic behavior can be found in many applications where until now only simplified technics are used for stability analysis and control design. Investigating mathematical methods that take into account explicitly the hybrid nature of these systems forms a challenging task both from engineering and mathematical point of view.


• Task 2: Switched systems with state and control discontinuities
  Responsible : Sophie Tarbouriech (CNRS - LAAS)
  
  As mentioned in Task 1, stability analysis of hybrid systems is already not so simple to handle. Although some important results are already available for general nonlinear hybrid systems, this important question remains open and is at a start. The analysis of the robustness issue with respect to uncertainties (such as measurement noise, model errors, or actuator disturbances) need to be precisely considered. Also the connection of hybrid systems with delay systems and in particular the robustness issue with respect to small delay should be considered. In this task, we focus on state and control discontinuities phenomena frequently encountered in practical applications.


• Task 3: Switched systems with performance constraints
  Responsible : Marc Jungers (CNRS - CRAN)
  
  The first questions arising naturally in the study of hybrid systems have concerned their stability or stabilizability. Even if there exits a considerable amount of scientific literature on this topic, it could be significantly improved and is still a widely open framework as indicated in task 1 and 2 in this project. Nevertheless the existing mature results help and allow to be ambitious by coping with additional specifications or constraints in the model of hybrid systems. By further specification or constraint, we mean input and output saturations and guaranteeing a standard (optimal or sub-optimal) level of performance.