This paper derives sufficient conditions for the stability of uncertain quasi-periodic hybrid dynamic systems. These conditions do not require the Lyapunov function to be non-increasing along each trajectory of the continuous variable dynamic system (CVDS), in other words, they do not require every CVDS to be stable, and they also do not require the Lyapunov function to be non-increasing along the whole sequence of the switchings. Furthermore, they do not require the knowledge of the continuous trajectory. With the proposed conditions, the stability bounds for structured perturbations characterized by non-negative matrices that still ensure robust stability are derived.