Hybrid dynamical systems are those with state variables that can flow  and/or jump. This talk gives an overview of a framework 
for analyzing  hybrid dynamical systems.  The emphasis is on a solution description  and modeling assumptions that guarantee 
"robustness", especially in  hybrid control systems. In such a setting, robustness refers to  successful feedback stabilization 
even in the presence of small  modeling errors, exogenous disturbances, and measurement noise. A  framework for "robust" hybrid 
systems will be introduced, and basic  properties of solutions will be described.  Then it will be shown how  these results lead 
to fundamental stability theory results for hybrid  systems, including invariance principles and converse Lyapunov  theorems.   
Finally, some applications of these principles to hybrid  feedback control design will be discussed.