Tools for Stability of Switching Linear Systems: Gain Automata and Delay Compensation.

Romanus Langerak; Jan W. Polderman

doi:10.1109/CDC.2005.1582932

Tools for Stability of Switching Linear Systems: Gain Automata and Delay Compensation.

Romanus Langerak
, Jan W. Polderman

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

9 Citations (Scopus)

381 Downloads (Pure)

Abstract

The topic of this paper is the analysis of stability for a class of switched linearsystems, modeled by hybrid automata. In each location of the hybrid automaton the dynamics is assumed to be linear and asymptotically stable; the guards on the transitions are hyperplanes in the state space. For each location an estimate is made of the gain via a Lyapunov function for the dynamics in that location, given a pair of ingoing and outgoing transitions. It is shown how to obtain the best possible estimate by optimizing the Lyapunov function. The estimated 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. The associated gain automaton provides a systematic tool to detect potential sources of instability as well as an indication on to how to stabilize the hybrid systems by requiring appropriate delays for specific transitions.

Original language	Undefined
Title of host publication	44th IEEE Conference on Decision and Control and European Control Conference ECC 2005
Place of Publication	Los Alamitos
Publisher	IEEE
Pages	4867-4872
Number of pages	6
ISBN (Print)	0-7803-9567-0
DOIs	https://doi.org/10.1109/CDC.2005.1582932
Publication status	Published - 11 Dec 2005
Event	44th Conference on Decision and Control, and 2005 European Control Conference, CDC-ECC 2005 - Melia Seville, Seville, Spain Duration: 12 Dec 2005 → 15 Dec 2005 Conference number: 44

Publication series

Name
Publisher	IEEE

Conference

Conference	44th Conference on Decision and Control, and 2005 European Control Conference, CDC-ECC 2005
Abbreviated title	CDC-ECC
Country/Territory	Spain
City	Seville
Period	12/12/05 → 15/12/05

Keywords

Automata
EWI-1539
IR-54781
Switched systems
METIS-229270
Stability of hybrid systems

Access to Document

10.1109/CDC.2005.1582932

http://tinyurl.com/aq6sbb

Cite this

@inproceedings{8b51e346415d4ac6b76a577883861aac,

title = "Tools for Stability of Switching Linear Systems: Gain Automata and Delay Compensation.",

abstract = "The topic of this paper is the analysis of stability for a class of switched linearsystems, modeled by hybrid automata. In each location of the hybrid automaton the dynamics is assumed to be linear and asymptotically stable; the guards on the transitions are hyperplanes in the state space. For each location an estimate is made of the gain via a Lyapunov function for the dynamics in that location, given a pair of ingoing and outgoing transitions. It is shown how to obtain the best possible estimate by optimizing the Lyapunov function. The estimated 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. The associated gain automaton provides a systematic tool to detect potential sources of instability as well as an indication on to how to stabilize the hybrid systems by requiring appropriate delays for specific transitions.",

keywords = "Automata, EWI-1539, IR-54781, Switched systems, METIS-229270, Stability of hybrid systems",

author = "Romanus Langerak and Polderman, \{Jan W.\}",

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year = "2005",

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day = "11",

doi = "10.1109/CDC.2005.1582932",

language = "Undefined",

isbn = "0-7803-9567-0",

publisher = "IEEE",

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booktitle = "44th IEEE Conference on Decision and Control and European Control Conference ECC 2005",

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Langerak, R & Polderman, JW 2005, Tools for Stability of Switching Linear Systems: Gain Automata and Delay Compensation. in 44th IEEE Conference on Decision and Control and European Control Conference ECC 2005. IEEE, Los Alamitos, pp. 4867-4872, 44th Conference on Decision and Control, and 2005 European Control Conference, CDC-ECC 2005, Seville, Spain, 12/12/05. https://doi.org/10.1109/CDC.2005.1582932

Tools for Stability of Switching Linear Systems: Gain Automata and Delay Compensation. / Langerak, Romanus; Polderman, Jan W.
44th IEEE Conference on Decision and Control and European Control Conference ECC 2005. Los Alamitos: IEEE, 2005. p. 4867-4872.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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N2 - The topic of this paper is the analysis of stability for a class of switched linearsystems, modeled by hybrid automata. In each location of the hybrid automaton the dynamics is assumed to be linear and asymptotically stable; the guards on the transitions are hyperplanes in the state space. For each location an estimate is made of the gain via a Lyapunov function for the dynamics in that location, given a pair of ingoing and outgoing transitions. It is shown how to obtain the best possible estimate by optimizing the Lyapunov function. The estimated 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. The associated gain automaton provides a systematic tool to detect potential sources of instability as well as an indication on to how to stabilize the hybrid systems by requiring appropriate delays for specific transitions.

AB - The topic of this paper is the analysis of stability for a class of switched linearsystems, modeled by hybrid automata. In each location of the hybrid automaton the dynamics is assumed to be linear and asymptotically stable; the guards on the transitions are hyperplanes in the state space. For each location an estimate is made of the gain via a Lyapunov function for the dynamics in that location, given a pair of ingoing and outgoing transitions. It is shown how to obtain the best possible estimate by optimizing the Lyapunov function. The estimated 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. The associated gain automaton provides a systematic tool to detect potential sources of instability as well as an indication on to how to stabilize the hybrid systems by requiring appropriate delays for specific transitions.

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