Abstract
It is shown that the existence of a continuous control-Lyapunov function (CLF) is necessary and sufficient for null asymptotic controllability of nonlinear finite-dimensional control systems. The CLF condition is expressed in terms of a concept of generalized derivative that has been studied in set-valued analysis and the theory of differential inclusions with various names such as 'upper contingent derivative.' This result generalizes to the non-smooth case the theorem of Artstein relating closed-loop feedback stabilization to smooth CLF's. It relies on viability theory as well as optimal control techniques. A 'non-strict' version of the results, analogous to the LaSalle Invariance Principle, is also provided.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 2799-2805 |
| Number of pages | 7 |
| Journal | Proceedings of the IEEE Conference on Decision and Control |
| Volume | 3 |
| State | Published - 1995 |
| Event | Proceedings of the 1995 34th IEEE Conference on Decision and Control. Part 1 (of 4) - New Orleans, LA, USA Duration: Dec 13 1995 → Dec 15 1995 |
All Science Journal Classification (ASJC) codes
- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization