Inscrição na biblioteca: Guest
Portal Digital Begell Biblioteca digital da Begell eBooks Diários Referências e Anais Coleções de pesquisa
Journal of Automation and Information Sciences
SJR: 0.275 SNIP: 0.59 CiteScore™: 0.8

ISSN Imprimir: 1064-2315
ISSN On-line: 2163-9337

Volumes:
Volume 52, 2020 Volume 51, 2019 Volume 50, 2018 Volume 49, 2017 Volume 48, 2016 Volume 47, 2015 Volume 46, 2014 Volume 45, 2013 Volume 44, 2012 Volume 43, 2011 Volume 42, 2010 Volume 41, 2009 Volume 40, 2008 Volume 39, 2007 Volume 38, 2006 Volume 37, 2005 Volume 36, 2004 Volume 35, 2003 Volume 34, 2002 Volume 33, 2001 Volume 32, 2000 Volume 31, 1999 Volume 30, 1998 Volume 29, 1997 Volume 28, 1996

Journal of Automation and Information Sciences

DOI: 10.1615/JAutomatInfScien.v51.i10.20
pages 23-30

On the Issue of Stability of Hybrid Automata by a Part of Variables

Alexey S. Bychkov
Kiev National Taras Shevchenko University, Kiev
Olga N. Suprun
Kiev National Taras Shevchenko University, Kiev
Irzhy Krzhyzh
Brno University of Technology, Brno (Czech Republic)
Veronika Navotna
Brno University of Technology, Brno (Czech Republic)

RESUMO

The problem of the stability of hybrid automata according to certain variables is considered. This problem is urgent and develops rapidly, especially in recent years. Aspects of its solution using the Lyapunov functions are also considered. The problem of hybrid automata stability regarding certain variables arises naturally for solving the applied problems. Namely, when based on the requirements of the normal functioning of an object, it is sufficient to ensure its stability only according to some variables. Formulation of the problem of stability regarding certain variables belongs to A.M. Lyapunov, but he himself did not investigate this problem. There is a great methodological similarity in the study of stability considering all, and a part of variables using the Lyapunov functions. However, there are certain differences in resolving some identical issues as applied to stability problems for all and a part of the variables. There are methods to reduce the problem of stability regarding certain variables to the study of stability in all variables of some auxiliary system, and vice versa. These two types of stability are closely related and mutually complementary. Currently, the problem of the stability of hybrid automata in terms of variables is considered as an independent section of the theory of stability. It is shown that the property of the y1-positive definiteness of Lyapunov functions is not sufficient for studying the stability of hybrid automata in terms of a part of variables. The concept of a y1-uniform positive definiteness of a function had been introduced. Theorems that provide sufficient stability conditions had been proved. For linear hybrid automata the constructive stability conditions had been obtained. The article also shows how using the stated theorems one can investigate the stability of hybrid timed automata.

Referências

  1. Roumiantsev V.V., Oziraner A.S., Stability and stabilization of motion relative to a part of variables [in Russian], Nauka, Moscow, 1987 .

  2. Bychkov A.S., Merkuriev M.G., Sufficient conditions of stability of stationary state of linear hybrid automata, Upravlyayushchie sistemy i mashiny, 2007, No. 2, 18-23, https//doi.org/10.15407/usim .

  3. Bychkov A.S., Ivanov E.V., Stability research of hybrid automata for modeling motion of flying apparatus, Upravlyayushchie sistemy i mashiny, 2008, No. 5, 24-28, 61, https//doi.org/ 10.15407/usim .

  4. Peleties P., DeCarlo R., Asymptotic stability of m-switched systems using Lyapunov functions, Proceedings of the 31st IEEE Conference on Decision and Control, Tucson, AZ, USA, 1992, 3438-3439, http://dx.doi.org/ 10.1109/cdc.1992.371213 .

  5. Pettersson S., Lennartson B., Stability and robustness for hybrid systems, Proceedings of the 35th Conference on Decision and Control, Kobe, Japan, 1996, 1202-1207, http://dx.doi.org/ 10.1109/CDC.1996.572653 .

  6. Ye H., Michel A., Hou L., Stability theory for hybrid dynamical systems, IEEE Transactions on Automatic Control, 43, No. 4, 1998, 461-474, http://dx.doi.0rg/10.l 109/9.664149 .

  7. Panayotova G., Dimitrov G.P., Petrov P., Bychkov O.S., Modeling and data processing of information systems, Proceedings of the Third International Conference on Artificial Intelligence and Pattern Recognition (AIPR), Lodz, Poland, 2016, 154-158, http://dx.doi.org/10.1109/ ICAIPR.2016.7585229 .

  8. Dimitrov G., Bychkov O., Petrov P., One approach for analysis of fuzzy linear hybrid automata, Izvestia Journal of the Union of Scientists-Varna, Economic Sciences Series, Union of Scientists Varna, Economic Sciences Section, 2018, 7(2), 234-240, Handle: RePEc: vra:journl:v:7:y:2018: i:2:p:234-240 .


Articles with similar content:

Pontryagin First Direct Method for Differential Inclusions
Journal of Automation and Information Sciences, Vol.52, 2020, issue 2
Ikromjon M. Iskanadjiev
Robust stability and Synthesis of Discrete
Journal of Automation and Information Sciences, Vol.39, 2007, issue 7
Vsevolod M. Kuntsevich
On Nonstationary Problem of Motion Control in Conflict Situation
Journal of Automation and Information Sciences, Vol.51, 2019, issue 7
Alexey A. Chikriy, Kirill A. Chikriy, Vladimir A. Pepelyaev
Conditions of Technical Stability of Autonomous Control Systems with Variable Structure
Journal of Automation and Information Sciences, Vol.31, 1999, issue 12
Konstantin S. Matviychuk
On Solution of Continuous Stochastic Problem of Optimal Partitioning with Objective Functional Recovery
Journal of Automation and Information Sciences, Vol.32, 2000, issue 3
Elena M. Kiseleva, Konstantin A. Kuznetsov