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Results on existence of smooth Lyapunov functions for (pre-)asymptotically stable hybrid systems with non-open basins of attraction | IEEE Conference Publication | IEEE Xplore

Results on existence of smooth Lyapunov functions for (pre-)asymptotically stable hybrid systems with non-open basins of attraction


Abstract:

We show that (pre-)asymptotic stability, which is a natural generalization of asymptotic stability, of a compact set for a hybrid system satisfying mild regularity assump...Show More

Abstract:

We show that (pre-)asymptotic stability, which is a natural generalization of asymptotic stability, of a compact set for a hybrid system satisfying mild regularity assumptions is equivalent to the existence of a smooth Lyapunov function. In this new converse Lyapunov theorem for (pre-)asymptotic stability, we no longer require the assumption that the basin of attraction is open (cf. [1, Theorem 1]). Furthermore, we demonstrate several applications of the converse Lyapunov theorem by establishing robustness of pre-asymptotic stability to various types of perturbations and achieving input-to-state stabilization for hybrid-feedback-control systems.
Date of Conference: 09-13 July 2007
Date Added to IEEE Xplore: 30 July 2007
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Conference Location: New York, NY, USA

References

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