Abstract
We present a sufficient condition for asymptotic stability of a switched linear system in terms of the Lie algebra generated by the individual matrices. Namely, if this Lie algebra is solvable, then the switched system is exponentially stable for arbitrary switching. In fact, we show that any family of linear systems satisfying this condition possesses a quadratic common Lyapunov function. We also discuss the implications of this result for switched nonlinear systems.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 117-122 |
| Number of pages | 6 |
| Journal | Systems and Control Letters |
| Volume | 37 |
| Issue number | 3 |
| DOIs | |
| State | Published - Jul 1999 |
| Externally published | Yes |
Keywords
- Quadratic common Lyapunov function
- Switched system
- Uniform exponential stability
ASJC Scopus subject areas
- Control and Systems Engineering
- Computer Science(all)
- Mechanical Engineering
- Electrical and Electronic Engineering