This paper presents a stability analysis approach for a class of hybrid automata. It is assumed that the dynamics in each location of the hybrid automaton is linear and asymptotically stable, and that the guards on the transitions are hyperplanes in the state space. For each pair of ingoing and outgoing transitions in a location a conservative estimate is made of the gain via a Lyapunov function for the dynamics in that location. It is shown how the choice of the Lyapunov function can be optimized to obtain the best possible estimate. The calculated conservative gains are used in defining a so-called gain automaton that forms the basis of an algorithmic criterion for the stability of the hybrid automaton.
|Number of pages||6|
|Publication status||Published - 2003|
|Event||IFAC Conference on Analysis and Design of Hybrid Systems, ADHS 2003 - Saint Malo, France|
Duration: 16 Jun 2003 → 18 Jun 2003
|Conference||IFAC Conference on Analysis and Design of Hybrid Systems, ADHS 2003|
|Period||16/06/03 → 18/06/03|
Langerak, R., Engell, S. (Ed.), Guegen, H. (Ed.), Polderman, J. W., Krilavicius, T., & Zaytoon, J. (Ed.) (2003). Stability Analysis for Hybrid Automata Using Conservative Gains. 377-382. Paper presented at IFAC Conference on Analysis and Design of Hybrid Systems, ADHS 2003, Saint Malo, France.