Stability Analysis for Hybrid Automata Using Conservative Gains

Romanus Langerak; S. Engell; H. Guegen; Jan W. Polderman; T. Krilavicius; J. Zaytoon

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 language	Undefined
Pages	377-382
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

Conference	IFAC Conference on Analysis and Design of Hybrid Systems, ADHS 2003
Abbreviated title	ADHS
Country	France
City	Saint Malo
Period	16/06/03 → 18/06/03

Keywords

IR-66637
EWI-8240

Access to Document

adhs03
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adhs03
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Cite this

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title = "Stability Analysis for Hybrid Automata Using Conservative Gains",

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.",

keywords = "IR-66637, EWI-8240",

author = "Romanus Langerak and S. Engell and H. Guegen and Polderman, {Jan W.} and T. Krilavicius and J. Zaytoon",

year = "2003",

language = "Undefined",

pages = "377--382",

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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

Y2 - 16 June 2003 through 18 June 2003

ER -