Relaxed stabilizability conditions for hybrid linear systems on periodic time domains

In this paper, we consider the problem of designing stabilizing feedback control laws for hybrid linear systems defined on periodic time domains. In this context, requiring the existence of a Lyapunov function decreasing simultaneously along flow and jump dynamics is a rather conservative condition. We propose then relaxed conditions for analysis and design that allow to systematically redistribute negativity of a candidate Lyapunov function between the continuous-time and the discrete-time compo- nents. Interestingly, such redistribution is performed dynamically by suitably assigning the behavior over the time interval of a time-varying component of the function. Finally, it is shown that the latter selection, in the design scenario, may be recast in terms of a reachability problem for a LTI extended system.