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Stabhyli: a tool for automatic stability verification of non-linear hybrid systems

Authors:

Eike Möhlmann,

Oliver TheelAuthors Info & Claims

HSCC '13: Proceedings of the 16th international conference on Hybrid systems: computation and control

Pages 107 - 112

https://doi.org/10.1145/2461328.2461347

Published: 08 April 2013 Publication History

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Abstract

We present Stabhyli, a tool that automatically proves stability of non-linear hybrid systems. Hybrid systems are systems that exhibit discrete as well as continuous behavior. The stability property basically ensures that a system exposed to a faulty environment (e.g. suffering from disturbances) will be able to regain a "good" operation mode as long as errors occur not too frequently. Stabilizing Hybrid systems are omnipresent, for instance in control applications where a discrete controller is controlling a time-continuous process such as a car's movement or a particular chemical reaction. We have implemented a tool to automatically derive a certificate of stability for non-linear hybrid systems. Certificates are obtained by Lyapunov theory combined with decomposition and composition techniques.

References

[1]

B. Borchers. Csdp, a C library for semidefinite programming. Optim. Met. Softw., 10:613--623, 1999.

Crossref

Google Scholar

[2]

S. Boyd and L. Vandenberghe. Convex Optimization. Cambridge University Press, Mar. 2004.

Digital Library

Google Scholar

[3]

W. Damm, H. Dierks, J. Oehlerking, and A. Pnueli. Towards Component Based Design of Hybrid Systems: Safety and Stability. In Essays in Memory of Amir Pnueli, volume 6200 of LNCS, pages 96--143. Springer, 2010.

Digital Library

Google Scholar

[4]

P. S. Duggirala and S. Mitra. Lyapunov abstractions for inevitability of hybrid systems. In HSCC, pages 115--124. ACM, 2012.

Digital Library

Google Scholar

[5]

M. Franzle, H. Hungar, C. Schmitt, and B. Wirtz. Hlang: Compositional representation of hybrid systems via predicates. Reports of SFB/TR 14 AVACS 20, SFB/TR 14 AVACS, July 2007. ISSN: 1860--9821, http://www.avacs.org.

Google Scholar

[6]

M. Lyapunov. Problàme général de la stabilité du movement. In Ann. Fac. Sci. Toulouse, 9, pages 203--474. Université Paul Sabatier, 1907. (Translation of a paper published in Comm. Soc. Math. Kharkow, 1893, reprinted Ann. Math. Studies No. 17, Princeton Univ. Press, 1949).

Crossref

Google Scholar

[7]

J. Oehlerking. Decomposition of Stability Proofs for Hybrid Systems. PhD thesis, Carl von Ossietzky University of Oldenburg, Department of Computer Science, Oldenburg, Germany, 2011.

Google Scholar

[8]

J. Oehlerking, H. Burchardt, and O. E. Theel. Fully Automated Stability Verification for Piecewise Affine Systems. In HSCC, volume 4416 of LNCS, pages 741--745. Springer, 2007.

Digital Library

Google Scholar

[9]

J. Oehlerking and O. E. Theel. Decompositional Construction of Lyapunov Functions for Hybrid Systems. In HSCC, volume 5469 of LNCS, pages 276--290. Springer, 2009.

Digital Library

Google Scholar

[10]

S. Pettersson. Analysis and Design of Hybrid Systems. PhD thesis, CTH, Gothenburg, Sweden, 1999.

Google Scholar

[11]

A. Podelski and S. Wagner. Region Stability Proofs for Hybrid Systems. In FORMATS, volume 4763 of LNCS, pages 320--335. Springer, 2007.

Digital Library

Google Scholar

[12]

S. Prajna and A. Papachristodoulou. Analysis of Switched and Hybrid Systems - Beyond Piecewise Quadratic Methods, 2003.

Google Scholar

[13]

S. Ratschan and Z. She. Providing a Basin of Attraction to a Target Region of Polynomial Systems by Computation of Lyapunov-Like Functions. SIAM J. Control and Optimization, 48(7):4377--4394, 2010.

Digital Library

Google Scholar

[14]

S. Warshall. A Theorem on Boolean Matrices. Journal of the ACM, 9:11--12, 1962.

Digital Library

Google Scholar

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Basagiannis SBattista LBecchi ACimatti AGiantamidis GMover STacchella ATonetta STsachouridis V(2023)SMT-Based Stability Verification of an Industrial Switched PI Control Systems2023 53rd Annual IEEE/IFIP International Conference on Dependable Systems and Networks Workshops (DSN-W)10.1109/DSN-W58399.2023.00063(243-250)Online publication date: Jun-2023
https://doi.org/10.1109/DSN-W58399.2023.00063
Tan YMitsch SPlatzer ABartocci EPutot S(2022)Verifying Switched System Stability With LogicProceedings of the 25th ACM International Conference on Hybrid Systems: Computation and Control10.1145/3501710.3519541(1-11)Online publication date: 4-May-2022
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Soto MPrabhakar P(2018)AveristProceedings of the 21st International Conference on Hybrid Systems: Computation and Control (part of CPS Week)10.1145/3178126.3178154(259-264)Online publication date: 11-Apr-2018
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Stabhyli: a tool for automatic stability verification of non-linear hybrid systems

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Published In

HSCC '13: Proceedings of the 16th international conference on Hybrid systems: computation and control

April 2013

378 pages

ISBN:9781450315678

DOI:10.1145/2461328

Program Chairs:
Calin Belta
Boston University, USA
,
Franjo Ivančić
NEC Laboratories America, USA

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: 08 April 2013

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HSCC '13: Computation and Control

April 8 - 11, 2013

Pennsylvania, Philadelphia, USA

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HSCC '13 Paper Acceptance Rate 40 of 86 submissions, 47%;

Overall Acceptance Rate 153 of 373 submissions, 41%

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Basagiannis SBattista LBecchi ACimatti AGiantamidis GMover STacchella ATonetta STsachouridis V(2023)SMT-Based Stability Verification of an Industrial Switched PI Control Systems2023 53rd Annual IEEE/IFIP International Conference on Dependable Systems and Networks Workshops (DSN-W)10.1109/DSN-W58399.2023.00063(243-250)Online publication date: Jun-2023
https://doi.org/10.1109/DSN-W58399.2023.00063
Tan YMitsch SPlatzer ABartocci EPutot S(2022)Verifying Switched System Stability With LogicProceedings of the 25th ACM International Conference on Hybrid Systems: Computation and Control10.1145/3501710.3519541(1-11)Online publication date: 4-May-2022
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Soto MPrabhakar P(2018)AveristProceedings of the 21st International Conference on Hybrid Systems: Computation and Control (part of CPS Week)10.1145/3178126.3178154(259-264)Online publication date: 11-Apr-2018
https://dl.acm.org/doi/10.1145/3178126.3178154
Sogokon AJackson PJohnson T(2018)Verifying Safety and Persistence in Hybrid Systems Using Flowpipes and Continuous InvariantsJournal of Automated Reasoning10.1007/s10817-018-9497-xOnline publication date: 24-Nov-2018
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Recommendations

Towards Push-of-a-Button Stability Verification for Discrete-Time Hybrid Systems

Switched discrete-time systems with time-varying delays: A generalized H2 approach

Stability and robust stabilization of 2-D continuous---discrete systems in Roesser model based on KYP lemma

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