Stability Analysis for Hybrid Automata Using Conservative Gains

Romanus Langerak, S. Engell (Editor), H. Guegen (Editor), Jan W. Polderman, T. Krilavicius, J. Zaytoon (Editor)

Research output: Contribution to conference › Paper › Academic › peer-review

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Abstract

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.
Original languageUndefined
Pages377-382
Number of pages6
Publication statusPublished - 2003
EventIFAC Conference on Analysis and Design of Hybrid Systems, ADHS 2003 - Saint Malo, France
Duration: 16 Jun 2003 → 18 Jun 2003

Conference

ConferenceIFAC Conference on Analysis and Design of Hybrid Systems, ADHS 2003
Abbreviated titleADHS
CountryFrance
CitySaint Malo
Period16/06/03 → 18/06/03

Keywords

  • IR-66637
  • EWI-8240

Cite this

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.
Langerak, Romanus ; Engell, S. (Editor) ; Guegen, H. (Editor) ; Polderman, Jan W. ; Krilavicius, T. ; Zaytoon, J. (Editor). / Stability Analysis for Hybrid Automata Using Conservative Gains. Paper presented at IFAC Conference on Analysis and Design of Hybrid Systems, ADHS 2003, Saint Malo, France.6 p.
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abstract = "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.",
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Langerak, R, Engell, S (ed.), Guegen, H (ed.), Polderman, JW, Krilavicius, T & Zaytoon, J (ed.) 2003, 'Stability Analysis for Hybrid Automata Using Conservative Gains' Paper presented at IFAC Conference on Analysis and Design of Hybrid Systems, ADHS 2003, Saint Malo, France, 16/06/03 - 18/06/03, pp. 377-382.

Stability Analysis for Hybrid Automata Using Conservative Gains. / Langerak, Romanus; Engell, S. (Editor); Guegen, H. (Editor); Polderman, Jan W.; Krilavicius, T.; Zaytoon, J. (Editor).

2003. 377-382 Paper presented at IFAC Conference on Analysis and Design of Hybrid Systems, ADHS 2003, Saint Malo, France.

Research output: Contribution to conference › Paper › Academic › peer-review

TY - CONF

T1 - Stability Analysis for Hybrid Automata Using Conservative Gains

AU - Langerak, Romanus

AU - Polderman, Jan W.

AU - Krilavicius, T.

A2 - Engell, S.

A2 - Guegen, H.

A2 - Zaytoon, J.

PY - 2003

Y1 - 2003

N2 - 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.

AB - 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.

KW - IR-66637

KW - EWI-8240

M3 - Paper

SP - 377

EP - 382

ER -

Langerak R, Engell S, (ed.), Guegen H, (ed.), Polderman JW, Krilavicius T, Zaytoon J, (ed.). Stability Analysis for Hybrid Automata Using Conservative Gains. 2003. Paper presented at IFAC Conference on Analysis and Design of Hybrid Systems, ADHS 2003, Saint Malo, France.

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