Construction of Lyapunov Functions for Switched Systems using Meshfree Collocation
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866913180519759872 |
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| author | Ward, Jay Georgiou, Nicos Giesl, Peter |
| author_facet | Ward, Jay Georgiou, Nicos Giesl, Peter |
| contents | Switched systems are a family of dynamical systems where a switching rule indicates which system is "switched on". This rule can be dependent on time and/or position in the state space. Stability of switched systems is a property that is often investigated using the existence of one (or multiple) Lyapunov function(s). We develop an algorithm using a scattered approximation method to construct a Lyapunov function for switched systems, accompanied with stability results. The construction adapts a previous method for autonomous ODEs that uses meshfree collocation and quadratic programming. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_02495 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Construction of Lyapunov Functions for Switched Systems using Meshfree Collocation Ward, Jay Georgiou, Nicos Giesl, Peter Dynamical Systems 93D30, 93-08 (Primary) 34D20, 90C20 (Secondary) Switched systems are a family of dynamical systems where a switching rule indicates which system is "switched on". This rule can be dependent on time and/or position in the state space. Stability of switched systems is a property that is often investigated using the existence of one (or multiple) Lyapunov function(s). We develop an algorithm using a scattered approximation method to construct a Lyapunov function for switched systems, accompanied with stability results. The construction adapts a previous method for autonomous ODEs that uses meshfree collocation and quadratic programming. |
| title | Construction of Lyapunov Functions for Switched Systems using Meshfree Collocation |
| topic | Dynamical Systems 93D30, 93-08 (Primary) 34D20, 90C20 (Secondary) |
| url | https://arxiv.org/abs/2606.02495 |