Abstract
A general upper bound for topological entropy of switched nonlinear systems is constructed, using an asymptotic average of upper limits of the matrix measures of Jacobian matrices of strongly persistent individual modes, weighted by their active rates. A general lower bound is constructed as well, using a similar weighted average of lower limits of the traces of these Jacobian matrices. In a case of interconnected structure, the general upper bound is readily applied to derive upper bounds for entropy that depend only on “network-level” information. In a case of block-diagonal structure, less conservative upper and lower bounds for entropy are constructed. In each case, upper bounds for entropy that require less information about the switching signal are also derived. The upper bounds for entropy and their relations are illustrated by numerical examples of a switched Lotka–Volterra ecosystem model.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 641-683 |
| Number of pages | 43 |
| Journal | Mathematics of Control, Signals, and Systems |
| Volume | 35 |
| Issue number | 3 |
| DOIs | |
| State | Published - Sep 2023 |
| Externally published | Yes |
Keywords
- Interconnected systems
- Nonlinear systems
- Switched systems
- Topological entropy
ASJC Scopus subject areas
- Control and Systems Engineering
- Signal Processing
- Control and Optimization
- Applied Mathematics