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Submersive rational difference systems and their accessibility

Authors:

Miroslav Halás,

Chunming YuanAuthors Info & Claims

ISSAC '09: Proceedings of the 2009 international symposium on Symbolic and algebraic computation

Pages 175 - 182

https://doi.org/10.1145/1576702.1576728

Published: 28 July 2009 Publication History

Abstract

The paper describes an algebraic construction of the inversive difference field associated with a discrete-time rational nonlinear control system under the assumption that the system is submersive. We prove that a system is submersive iff its associated difference ideal is proper, prime and reflexive. Next, we show that Kähler differentials of the above inversive field define a module over the corresponding ring of Ore operators, and relate its torsion submodule to the vector space of autonomous one-forms, introduced elsewhere. The above results allow us to check accessibility property and simplify transfer functions with computer algebra techniques.

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Cited By

Mullari TKotta UBartosiewicz ZPawluszewicz EMoog C(2017)Forward and Backward Shifts of Vector Fields: Towards the Dual Algebraic FrameworkIEEE Transactions on Automatic Control10.1109/TAC.2016.260871862:6(3029-3033)Online publication date: Jun-2017
https://doi.org/10.1109/TAC.2016.2608718
Kaldmäe AKotta ÜShumsky AZhirabok A(2014)Disturbance decoupling for nonlinear systems by measurement feedback: sensor locationIFAC Proceedings Volumes10.3182/20140824-6-ZA-1003.0001347:3(7729-7734)Online publication date: 2014
https://doi.org/10.3182/20140824-6-ZA-1003.00013
Cheng HLabahn G(2014)A Practical Implementation of a Modular Algorithm for Ore Polynomial MatricesComputer Mathematics10.1007/978-3-662-43799-5_5(49-59)Online publication date: 1-Oct-2014
https://doi.org/10.1007/978-3-662-43799-5_5
Show More Cited By

Index Terms

Submersive rational difference systems and their accessibility
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
      1. Algebraic algorithms

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cover image ACM Conferences

ISSAC '09: Proceedings of the 2009 international symposium on Symbolic and algebraic computation

July 2009

402 pages

ISBN:9781605586090

DOI:10.1145/1576702

General Chairs:
Jeremy Johnson
Drexel University, USA
,
Hyungju Park
Korea Institute for Advanced Study, Korea
,
Program Chair:
Erich Kaltofen
North Carolina State University, USA

Copyright © 2009 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 28 July 2009

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ISSAC '09: International Symposium on Symbolic and Algebraic Computation

July 28 - 31, 2009

Seoul, Republic of Korea

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Cited By

Mullari TKotta UBartosiewicz ZPawluszewicz EMoog C(2017)Forward and Backward Shifts of Vector Fields: Towards the Dual Algebraic FrameworkIEEE Transactions on Automatic Control10.1109/TAC.2016.260871862:6(3029-3033)Online publication date: Jun-2017
https://doi.org/10.1109/TAC.2016.2608718
Kaldmäe AKotta ÜShumsky AZhirabok A(2014)Disturbance decoupling for nonlinear systems by measurement feedback: sensor locationIFAC Proceedings Volumes10.3182/20140824-6-ZA-1003.0001347:3(7729-7734)Online publication date: 2014
https://doi.org/10.3182/20140824-6-ZA-1003.00013
Cheng HLabahn G(2014)A Practical Implementation of a Modular Algorithm for Ore Polynomial MatricesComputer Mathematics10.1007/978-3-662-43799-5_5(49-59)Online publication date: 1-Oct-2014
https://doi.org/10.1007/978-3-662-43799-5_5
Kawano YOhtsuka T(2013)Simple Sufficient Conditions for Reachability of Discrete-Time Polynomial SystemsIEEE Transactions on Automatic Control10.1109/TAC.2013.226118458:12(3203-3206)Online publication date: Dec-2013
https://doi.org/10.1109/TAC.2013.2261184
Belikov JKotta PKotta UTonso M(2012)Practical polynomial formulas in MIMO nonlinear realization problem2012 IEEE 51st IEEE Conference on Decision and Control (CDC)10.1109/CDC.2012.6427109(1253-1258)Online publication date: Dec-2012
https://doi.org/10.1109/CDC.2012.6427109
Kaldmae AKotta U(2012)Dynamic measurement feedback in discrete-time nonlinear control systems2012 American Control Conference (ACC)10.1109/ACC.2012.6314628(214-219)Online publication date: Jun-2012
https://doi.org/10.1109/ACC.2012.6314628
Kotta ÜTõnso M(2012)Realization of discrete-time nonlinear input–output equations: Polynomial approachAutomatica10.1016/j.automatica.2011.07.01048:2(255-262)Online publication date: Feb-2012
https://doi.org/10.1016/j.automatica.2011.07.010
Kotta ÜBartosiewicz ZNomm SPawluszewicz E(2011)Linear Input-Output Equivalence and Row Reducedness of Discrete-Time Nonlinear SystemsIEEE Transactions on Automatic Control10.1109/TAC.2011.211243056:6(1421-1426)Online publication date: Jun-2011
https://doi.org/10.1109/TAC.2011.2112430
Belikov JHalas MKotta UMoog C(2011)Model matching problem for discrete-time nonlinear systems: Transfer function approach2011 9th IEEE International Conference on Control and Automation (ICCA)10.1109/ICCA.2011.6137955(360-365)Online publication date: Dec-2011
https://doi.org/10.1109/ICCA.2011.6137955
Kotta UKotta PTonso MHalas M(2011)State-space realization of nonlinear input-output equations: Unification and extension via pseudo-linear algebra2011 9th IEEE International Conference on Control and Automation (ICCA)10.1109/ICCA.2011.6137881(354-359)Online publication date: Dec-2011
https://doi.org/10.1109/ICCA.2011.6137881
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