Commutativity and asymptotic stability for linear switched DAEs

Daniel Liberzon; Stephan Trenn; Fabian Wirth

doi:10.1109/CDC.2011.6160335

Commutativity and asymptotic stability for linear switched DAEs

Daniel Liberzon^*, Stephan Trenn, Fabian Wirth

^*Corresponding author for this work

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

22 Citations (Scopus)

Abstract

For linear switched ordinary differential equations with asymptotically stable constituent systems, it is well known that commutativity of the coefficient matrices implies asymptotic stability of the switched system under arbitrary switching. This result is generalized to linear switched differential algebraic equations (DAEs). Although the solutions of a switched DAE can exhibit jumps it turns out that it suffices to check commutativity of the "flow" matrices. As in the ODE case we are also able to construct a common quadratic Lyapunov function.

Original language	English
Title of host publication	2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Pages	417-422
Number of pages	6
DOIs	https://doi.org/10.1109/CDC.2011.6160335
Publication status	Published - 2011
Externally published	Yes
Event	2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 - Orlando, FL, United States Duration: 12-Dec-2011 → 15-Dec-2011

Conference

Conference	2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Country/Territory	United States
City	Orlando, FL
Period	12/12/2011 → 15/12/2011

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title = "Commutativity and asymptotic stability for linear switched DAEs",

abstract = "For linear switched ordinary differential equations with asymptotically stable constituent systems, it is well known that commutativity of the coefficient matrices implies asymptotic stability of the switched system under arbitrary switching. This result is generalized to linear switched differential algebraic equations (DAEs). Although the solutions of a switched DAE can exhibit jumps it turns out that it suffices to check commutativity of the {"}flow{"} matrices. As in the ODE case we are also able to construct a common quadratic Lyapunov function.",

author = "Daniel Liberzon and Stephan Trenn and Fabian Wirth",

year = "2011",

doi = "10.1109/CDC.2011.6160335",

language = "English",

isbn = "9781612848006",

pages = "417--422",

booktitle = "2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011",

note = "2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 ; Conference date: 12-12-2011 Through 15-12-2011",

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Liberzon, D, Trenn, S & Wirth, F 2011, Commutativity and asymptotic stability for linear switched DAEs. in 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011., 6160335, pp. 417-422, 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011, Orlando, FL, United States, 12/12/2011. https://doi.org/10.1109/CDC.2011.6160335

TY - GEN

T1 - Commutativity and asymptotic stability for linear switched DAEs

AU - Liberzon, Daniel

AU - Trenn, Stephan

AU - Wirth, Fabian

PY - 2011

Y1 - 2011

N2 - For linear switched ordinary differential equations with asymptotically stable constituent systems, it is well known that commutativity of the coefficient matrices implies asymptotic stability of the switched system under arbitrary switching. This result is generalized to linear switched differential algebraic equations (DAEs). Although the solutions of a switched DAE can exhibit jumps it turns out that it suffices to check commutativity of the "flow" matrices. As in the ODE case we are also able to construct a common quadratic Lyapunov function.

AB - For linear switched ordinary differential equations with asymptotically stable constituent systems, it is well known that commutativity of the coefficient matrices implies asymptotic stability of the switched system under arbitrary switching. This result is generalized to linear switched differential algebraic equations (DAEs). Although the solutions of a switched DAE can exhibit jumps it turns out that it suffices to check commutativity of the "flow" matrices. As in the ODE case we are also able to construct a common quadratic Lyapunov function.

UR - http://www.scopus.com/inward/record.url?scp=84860691258&partnerID=8YFLogxK

U2 - 10.1109/CDC.2011.6160335

DO - 10.1109/CDC.2011.6160335

M3 - Conference contribution

AN - SCOPUS:84860691258

SN - 9781612848006

SP - 417

EP - 422

BT - 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011

T2 - 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011

Y2 - 12 December 2011 through 15 December 2011

ER -

Commutativity and asymptotic stability for linear switched DAEs

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