Topological Entropy of Nonlinear Time-Varying Systems
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866918142495686656 |
|---|---|
| author | Yang, Guosong Liberzon, Daniel |
| author_facet | Yang, Guosong Liberzon, Daniel |
| contents | Two general upper bounds on the topological entropy of nonlinear time-varying systems are established: one using the matrix measure of the system Jacobian, the other using the largest real part of the eigenvalues of the Jacobian matrix with off-diagonal entries replaced by their absolute values. A general lower bound is constructed using the trace of the Jacobian matrix. For interconnected systems, an upper bound is first derived by adapting one of the general upper bounds, using the matrix measure of an interconnection matrix function. A new upper bound is then developed using the largest real part of the eigenvalues of this function. This new bound is closely related to the individual upper bounds for subsystems and implies each of the two general upper bounds when the system is viewed as one of two suitable interconnections. These entropy bounds all depend only on upper or lower limits of the Jacobian matrix along trajectories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_13537 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Topological Entropy of Nonlinear Time-Varying Systems Yang, Guosong Liberzon, Daniel Optimization and Control Systems and Control Dynamical Systems 37B40, 93C10 (Primary) 37B55, 93B70 (Secondary) Two general upper bounds on the topological entropy of nonlinear time-varying systems are established: one using the matrix measure of the system Jacobian, the other using the largest real part of the eigenvalues of the Jacobian matrix with off-diagonal entries replaced by their absolute values. A general lower bound is constructed using the trace of the Jacobian matrix. For interconnected systems, an upper bound is first derived by adapting one of the general upper bounds, using the matrix measure of an interconnection matrix function. A new upper bound is then developed using the largest real part of the eigenvalues of this function. This new bound is closely related to the individual upper bounds for subsystems and implies each of the two general upper bounds when the system is viewed as one of two suitable interconnections. These entropy bounds all depend only on upper or lower limits of the Jacobian matrix along trajectories. |
| title | Topological Entropy of Nonlinear Time-Varying Systems |
| topic | Optimization and Control Systems and Control Dynamical Systems 37B40, 93C10 (Primary) 37B55, 93B70 (Secondary) |
| url | https://arxiv.org/abs/2509.13537 |