Construction of Lyapunov functions from first integrals for stochastic stability analysis
| dc.contributor.author | Náprstek, Jiří | |
| dc.contributor.author | Fischer, Cyril | |
| dc.date.accessioned | 2026-01-15T08:37:47Z | |
| dc.date.available | 2026-01-15T08:37:47Z | |
| dc.date.issued | 2025 | |
| dc.description.abstract-translated | This paper explores the application of first integrals in constructing Lyapunov functions for stability analysis of dynamical systems in stochastic domains. A key advantage of using first integrals is their ability to embed system-specific structural and physical information, distinguishing the resulting Lyapunov functions from generic positive definite functions with no intrinsic connection to the system. However, since first integrals do not inherently satisfy Lyapunov conditions, additional constraints—often with direct physical interpretations—must be introduced to ensure positive definiteness and suitable monotonic behavior. The method is demonstrated on three mechanical systems subjected to parametric noise: a nonlinear aeroelastic single-degree-of-freedom oscillator, a spherical pendulum with two first integrals, and a gyroscope with three first integrals. | en |
| dc.description.sponsorship | The support of Czech Science Foundation project No. 24-13061S and of the RVO 68378297 institutional support are gratefully acknowledged. The authors used the ChatGPT language model (OpenAI) to assist with language polishing and proofreading; all suggestions were reviewed and revised to preserve the intended meaning. | |
| dc.format | 18 s. | cs |
| dc.format.mimetype | application/pdf | |
| dc.identifier.doi | https://doi.org/10.24132/acm.2025.1026 | |
| dc.identifier.issn | 1802-680X (Print) | |
| dc.identifier.issn | 2336-1182 (Online) | |
| dc.identifier.uri | http://hdl.handle.net/11025/64463 | |
| dc.language.iso | en | en |
| dc.publisher | University of West Bohemia | en |
| dc.rights | © University of West Bohemia | en |
| dc.rights.access | openAccess | en |
| dc.subject | stochastická stabilita | cs |
| dc.subject | Ljapunovova funkce | cs |
| dc.subject | první integrály | cs |
| dc.subject | cyklické souřadnice | cs |
| dc.subject.translated | stochastic stability | en |
| dc.subject.translated | Lyapunov function | en |
| dc.subject.translated | first integrals | en |
| dc.subject.translated | cyclic coordinates | en |
| dc.title | Construction of Lyapunov functions from first integrals for stochastic stability analysis | en |
| dc.type | článek | cs |
| dc.type | article | en |
| dc.type.status | Peer-reviewed | en |
| dc.type.version | publishedVersion | en |
| local.files.count | 1 | * |
| local.files.size | 663007 | * |
| local.has.files | yes | * |
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