What does this research mean for the field?

Dynamical systems possessing a continuum of equilibria can achieve finite-time and fixed-time semistability through homogeneous approximations in the bi-limit, which enables the design of fixed-time distributed consensus control protocols for multiagent networks. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

The research aims to explore homogeneous approximations in a geometric context and their implications for dynamical systems.

June 17, 2026Mathematics of Control Signals and SystemsOpen Access

Homogeneous approximations and fixed-time semistability with applications to network consensus

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Authors

KVKriti VermaGeorgia Institute of Technology WHWassim M. HaddadGeorgia Institute of Technology

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Implication

Develops homogeneous approximations to achieve fixed-time semistability in multiagent networks, suggesting new control protocols.

Key Points

The research aims to explore homogeneous approximations in a geometric context and their implications for dynamical systems.
Developed homogeneity concepts in 0-limit and infinity-limit under semi-Euler vector fields.
Analyzed regularity properties of functions and vector fields related to their homogeneity degree.
Derived finite and fixed time semistability results for dynamical systems with continuum equilibria.
Established new semistability results for dynamical systems influenced by homogeneous functions.
Created distributed consensus control protocols that enable fixed-time coordination in multiagent network systems.

Cite This Study

Verma et al. (2026) studied this question.

synapsesocial.com/papers/6a323915d50b63ecad204c33 https://doi.org/10.1007/s00498-026-00450-2

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Homogeneous approximations and fixed-time semistability with applications to network consensus

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Cite This Study

Homogeneous approximations and fixed-time semistability with applications to network consensus

Discussion

Member takes

Implication

Key Points

Cite This Study

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