List of English Publication

@inproceedings{nokey,

title = {Lyapunov Functions for Singularly Perturbed Hybrid Systems with Frequent Jump Dynamics},

author = {Aneel Tawani and Hyungbo Shim},

url = {https://css.paperplaza.net/conferences/conferences/CDC21/program/CDC21_ContentListWeb_4.html},

doi = {10.1109/CDC45484.2021.9682912},

year  = {2021},

date = {2021-12-13},

urldate = {2021-12-01},

booktitle = {Proc. of 2021 IEEE 60th Conference on Decision and Control},

pages = {5382-5387},

publisher = {IEEE},

address = {Austin, Texas, USA},

abstract = {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.},

keywords = {Hybrid system, Lyapunov function, Singular perturbation},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{ShimNhoSeo01,

title = {Common Lyapunov function for exponentially stable nonlinear systems},

author = {Hyungbo Shim and Daejong Noh and Jin Heon Seo},

url = {https://pdfs.semanticscholar.org/0605/0bf9470d9c45a6f4c7aabed1c9a3ee4a364f.pdf?_ga=2.158594426.1197052907.1568861989-778206293.1568861989},

year  = {2001},

date = {2001-01-01},

booktitle = {Proc. of 4th SIAM Conference on Control and Its Applications},

publisher = {SIAM},

organization = {SIAM},

abstract = {We present a sufficient condition for the existence of a common Lyapunov function for a family of exponentially stable nonlinear systems.

Suppose that there are m systems ˙x = fi(x) each of which is exponentially stable. When any pair of the vector fields fi(x) are commuting,

i.e. the Lie bracket of the pair is zero, there is one Lyapunov function V (x) which guarantees the exponential stability for all of them.},

keywords = {Lyapunov function},

pubstate = {published},

tppubtype = {inproceedings}

}