Abstract
We consider an open problem on the stability of nonlinear nilpotent switched systems posed by Daniel Liberzon. Partial solutions to this problem were obtained as corollaries of global nice reachability results for nilpotent control systems. The global structure is crucial in establishing stability. We show that a nice reachability analysis may be reduced to the reachability analysis of a specific canonical system, the nilpotent Hall-Sussmann system. Furthermore, local nice reachability properties for this specific system imply global nice reachability for general nilpotent systems. We derive several new results revealing the elegant Lie-algebraic structure of the nilpotent Hall-Sussmann system.
| Original language | English |
|---|---|
| Pages (from-to) | 766-772 |
| Number of pages | 7 |
| Journal | Systems and Control Letters |
| Volume | 58 |
| Issue number | 10-11 |
| DOIs | |
| State | Published - Oct 2009 |
Keywords
- Global asymptotic stability
- Lie bracket
- Maximum principle
- Nilpotent Lie algebra
- Nonlinear switched systems
- Optimal control
- P. Hall basis
- Reachability with nice controls
- Reachable sets
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