Robust stability of quasi-periodic hybrid dynamic uncertain systems

Considers the robust stability of quasi-periodic hybrid dynamic systems (HDSs) with polytopic uncertainties. The quasi-periodic HDSs has infinite switchings, but the switching sequence forms a cycle and the cycle is repeated. We derive the stability conditions for quasi-periodic HDS with uncertainties in continuous-variable dynamic systems, and with variations in both the “switching”-conditional set and the reset map by analyzing the behavior of the system along the cycle. The results require the Lyapunov function to be bounded by a continuous function along each continuous-variable dynamic system, and is nonincreasing along a subsequence of the “switchings.” They do not require the Lyapunov function to be nonincreasing along the whole sequence of the switchings