Polynomial Lyapunov Functions and Invariant Sets from a New Hierarchy of Quadratic Lyapunov Functions for LTV Systems
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909081230376960 |
|---|---|
| author | Abdelraouf, Hassan Feron, Eric Shamma, Jeff S. |
| author_facet | Abdelraouf, Hassan Feron, Eric Shamma, Jeff S. |
| contents | We introduce a new class of quadratic functions based on a hierarchy of linear time-varying (LTV) dynamical systems. These quadratic functions in the higher order space can be also seen as a non-homogeneous polynomial Lyapunov functions for the original system, i.e the first system in the hierarchy. These non-homogeneous polynomials are used to obtain accurate outer approximation for the reachable set given the initial condition and less conservative bounds for the impulse response peak of linear, possibly time-varying systems. In addition, we pose an extension to the presented approach to construct invariant sets that are not necessarily Lyapunov functions. The introduced methods are based on elementary linear systems theory and offer very much flexibility in defining arbitrary polynomial Lyapunov functions and invariant sets for LTV systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13128 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Polynomial Lyapunov Functions and Invariant Sets from a New Hierarchy of Quadratic Lyapunov Functions for LTV Systems Abdelraouf, Hassan Feron, Eric Shamma, Jeff S. Systems and Control We introduce a new class of quadratic functions based on a hierarchy of linear time-varying (LTV) dynamical systems. These quadratic functions in the higher order space can be also seen as a non-homogeneous polynomial Lyapunov functions for the original system, i.e the first system in the hierarchy. These non-homogeneous polynomials are used to obtain accurate outer approximation for the reachable set given the initial condition and less conservative bounds for the impulse response peak of linear, possibly time-varying systems. In addition, we pose an extension to the presented approach to construct invariant sets that are not necessarily Lyapunov functions. The introduced methods are based on elementary linear systems theory and offer very much flexibility in defining arbitrary polynomial Lyapunov functions and invariant sets for LTV systems. |
| title | Polynomial Lyapunov Functions and Invariant Sets from a New Hierarchy of Quadratic Lyapunov Functions for LTV Systems |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2401.13128 |