List of English Publication

@inproceedings{tran2026stabilityslowfastnonlineardynamics,

title = {Stability of Slow-Fast Nonlinear Dynamics: Non-Periodic Case},

author = {G. Q. Bao Tran / Daniel Liberzon / Hyungbo Shim},

url = {https://arxiv.org/abs/2606.18504},

doi = {10.48550/arXiv.2606.18504},

issn = {2405-8963},

year  = {2026},

date = {2026-08-17},

urldate = {2026-08-17},

booktitle = {27th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2026)},

pages = {127--132},

address = {Waterloo, ON, Canada},

organization = {International Federation of Automatic Control (IFAC)},

abstract = {We present sufficient conditions for the semi-global exponential stability of nonlinear systems whose dynamics have both slow and fast time variations. Unlike most existing results, the fast variation is non-periodic, thereby allowing a wider class of systems, especially switched systems with fast (non-periodic) switching and those with quasi-periodic variations; we therefore rely on general averaging to construct an average system. It is assumed that the average system admits a time-invariant equilibrium that is globally exponentially stable when the slow variation is frozen, i.e., remaining at a fixed value. This slow variation is allowed to be discontinuous in time, provided its total variation (flows and jumps) is bounded. The main result is illustrated using a nonlinear switched system with slow-fast non-periodic switching},

keywords = {Non-Linear Systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{nokey,

title = {Stability of Nonlinear Systems with Slow and Fast Time Variation and Switching: The Common Equilibrium Case},

author = {Daniel Liberzon and Hyungbo Shim},

doi = {10.1109/CDC56724.2024.10885786},

year  = {2024},

date = {2024-12-18},

urldate = {2024-12-18},

booktitle = {2024 IEEE 63rd Conference on Decision and Control (CDC)},

publisher = {IEEE},

address = {Milan, Italy},

abstract = {In this paper we consider a class of nonlinear systems with two kinds of inputs: one is slowly-varying, the other is fast-varying and periodic, and both are only piecewise continuous. Under the assumption that the origin is a common equilibrium for all values of the input signals, we provide sufficient conditions under which this equilibrium is semi-globally exponentially stable. Our approach is based on considering the (partial) average system which averages out the fast variation but retains the slow variation, and which can be used to approximate the original system in a certain sense. The stability conditions involve the existence of a suitable Lyapunov function for this average system, along with a bound on the total variation of the slowly-varying input.},

keywords = {Non-Linear Systems, Switched system},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{nokey,

title = {Stability Analysis of Nonlinear Systems Over Switching Networks Using Singularly Perturbed Hybrid Systems Framework},

author = {Andrew Teel and Aneel Tanwani and Hyungbo Shim},

url = {https://mtns2024.eng.cam.ac.uk/wp-content/uploads/2024/08/MTNS2024_Final_Programme.pdf},

year  = {2024},

date = {2024-08-20},

urldate = {2024-08-20},

booktitle = {26th International Symposium on Mathematical Theory of Networks and Systems},

publisher = {MTNS},

address = {cambridge,UK},

abstract = {To analyze the stability of a network of agents described by 

nonlinear oscillators which only exchange information about their 

position with some of its neighbors from time to time, we consider 

a theoretical framework of singularly perturbed hybrid systems. 

We describe such systems as an interconnection of two hybrid 

subsystems, a timer which triggers the jumps, and some discrete 

variables to determine the index of the jump maps. The flow 

equations of these variables are singularly perturbed differential 

equations, and in particular, smaller value of the singular 

perturbation parameter leads to increase in the frequency of the 

jump instants. For the limiting value of this parameter, we consider 

a decomposition which comprises a quasi-steady-state system 

modeled by a differential equation without any jumps, and a 

boundary-layer system described by purely discrete dynamics. 

Under appropriate stability assumptions on the quasi-steady-state 

system and the boundary-layer system, we derive results showing 

practical stability of a compact attractor when the information 

exchange between the agents occurs frequently often. },

keywords = {Hybrid system, Multi-agent system, Non-Linear Systems},

pubstate = {published},

tppubtype = {inproceedings}

}