Stability analysis of hybrid systems with time-varying delayed perturbations via single Lyapunov function

The design approach of the switching law, for a class of hybrid systems with time-varying perturbations in the time-delayed state, is presented to guarantee the asymptotic stability. Since these approaches can be expressed as linear matrix inequalities (LMIs) that can be solved easily, the corresponding LMI-based algorithms for determining stability bounds are derived. The example is given to demonstrate the effectiveness of the proposed approaches.