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Communication Dans Un Congrès Année : 2021

Lyapunov Functions for Singularly Perturbed Hybrid Systems with Frequent Jump Dynamics

Résumé

This article considers the stability analysis for a class of hybrid systems with the focus being on the frequently occurring jump dynamics. The system class is modelled as a singularly perturbed hybrid system where the singular perturbation parameter governs the frequency of jumps. Consequently, this results in a quasi steady-state system modeled by a differential equation without any jumps, and the boundary-layer system described by purely discrete dynamics. By imposing appropriate assumptions on the quasi steady-state system and the boundary-layer system, we derive results showing practical convergence to a compact attractor when the jumps occur frequently often. Our system class is motivated by the control design problem in a network of second-order continuous-time coupled oscillators, where each agent communicates the information about its position to the neighbors at discrete times. As a corollary to our main result, we show that if the information exchange between the agents and their neighbors is frequent enough, then the oscillators achieve practical consensus.
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Dates et versions

hal-03476840 , version 1 (30-12-2021)

Identifiants

Citer

Aneel Tanwani, Hyungbo Shim. Lyapunov Functions for Singularly Perturbed Hybrid Systems with Frequent Jump Dynamics. IEEE Conference on Decision and Control (CDC 2021), Dec 2021, Austin, Texas, United States. ⟨10.1109/CDC45484.2021.9682912⟩. ⟨hal-03476840⟩
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