## Section: New Results

### Hybrid dynamical systems

Participants : Wilfrid Perruquetti, Lotfi Belkoura, Thierry Floquet, Yang Tian.

Concerning hybrid dynamical systems, during the year 2009, we firstly extended our previous work on the estimation of the switching signal and of the state for switching linear systems [86] to the perturbed case when the perturbation is structured that is when the perturbation is unknown but known to satisfy a certain differential equation (for example if the perturbation is constant then its time-derivative is zero) (see [47] ). At the same time, we characterized singular inputs and/or perturbations for which the switched systems become undistinguishable.

Secondly, since the knowledge of the switching function plays a central role in observation and control of switched systems, we have developed, within the framework of ALIEN techniques (by using some algebraic manipulations), new algorithms in order to estimate in "real-time" the switching time sequence of some classes of switched linear systems with the knowledge of the continuous state only (see [47] , [62] , [63] ).