Uniform asymptotic stability of hybrid dynamical systems with delay

In this present note, we formulate a model for hybrid dynamical systems with delay, which covers a large class of delay systems. Under several mild assumptions, we establish sufficient conditions for uniform asymptotic stability of hybrid dynamical systems with delay via Lyapunov–Razumikhin technique. To demonstrate the developed theory, we conduct stability analyzes for delay sampled-data feedback control systems including a nonlinear continuous-time plant and a linear discrete-time controller.