Compositional Contraction Analysis of Resetting Hybrid Systems

This note develops sufficient conditions for exponential convergence of resetting hybrid nonlinear dynamical systems. Using nonlinear contraction theory, the analysis first develops a unified formulation of continuous-time and discrete-time nonlinear dynamics based on a differential transition matrix. This yields enhanced dwell-time based conditions for stability of such systems analogous to those existing for switched systems. It turns out that such dwell-time based conditions, unlike their counterparts for switched systems, include arbitrary stability conditions as a special case, and are less conservative and much simpler to verify