Abstract
Abstract Stability properties of singularly perturbed hybrid systems are investigated via Lyapunov functions with assistance from the invariance principle. Both continuously differentiable Lyapunov functions and non-smooth Lyapunov functions are considered. In each case, under appropriate assumptions, uniform asymptotic stability and uniform global asymptotic stability are established. An estimate of the basin of attraction is given for the former property. Two examples are given to illustrate the proposed theoretical results based on continuously differentiable Lyapunov functions. In addition, one example for switched learning inclusions with unstable modes is given to show the effectiveness of the results obtained based on non-smooth Lyapunov functions.
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