*Researchers*: S. Almér and U. Jönsson, and C.-Y. Kao in
collaboration with H. Fujioka, Kyoto University, L. Iannelli,
University of Napoli Federico II, K. H. Johansson, KTH, J. Mari,
GE Global Research, Munchen, F. Vasca, Universitá del Sannio in
Benevento.

*Sponsor*: Partly sponsored by the HYCON Network of Excellence, E. C:
grant IST-511368.

In this project we consider various problems in switched and hybrid systems. We are currently focusing on two problem areas in this field. The first is averaging theory for switched dynamical systems subject to external excitation. High frequency control signals and averaging theory is used in many control applications. The idea is that a systematic high frequency variation of the vector field can improve the controllability and simplify the control design. Averaging theory for discontinuous systems have been restricted to systems with particular nonlinearities and/or excitation signals. We are considering a general class of switched systems subject to excitation signals with Lipschitz continuous amplitude distribution function.

The second area is the design and analysis of pulse width modulated (PWM) control systems. Here we consider applications, such as switched DC-DC converters in high power applications, where averaging theory does not provide a sufficiently good approximation of the system dynamics to allow accurate design and analysis. This is an interesting class of switched systems where the switching is periodic but with varying duty rate, i.e. the proportion in which the different dynamics are active is varying from one period to another.