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Abstrakty
This paper deals with stability analysis of hybrid systems. Various stability concepts related to hybrid systems are introduced. The paper advocates a local analysis. It involves the equivalence relation generated by reset maps of a hybrid system. To establish a tangible method for stability analysis, we introduce the notion of a chart, which locally reduces the complexity of the hybrid system. In a chart, a hybrid system is particularly simple and can be analyzed with the use of methods borrowed from the theory of differential inclusions. Thus, the main contribution of this paper is to show how stability of a hybrid system can be reduced to a specialization of the well established stability theory of differential inclusions. A number of examples illustrate the concepts introduced in the paper.
Rocznik
Tom
Strony
341--355
Opis fizyczny
Bibliogr. 34 poz., rys.
Twórcy
autor
- Department of Electronic Systems, Automation and Control, Aalborg University, Fredrik Bajers Vej 7 C, 9220 Aalborg East, Denmark
autor
- Department of Electronic Systems, Automation and Control, Aalborg University, Fredrik Bajers Vej 7 C, 9220 Aalborg East, Denmark
Bibliografia
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- [5] Bujorianu, M.L. and Lygeros, J. (2006). Toward a general theory of stochastic hybrid systems, in H. Bloom and J. Lygeros (Eds.), Stochastic Hybrid Systems, Lecture Notes in Control and Information Sciences, Vol. 337, Springer, Berlin, pp. 3–30.
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- [8] Goebel, R. and Teel, A. R. (2006). Solutions to hybrid inclusions via set and graphical convergence with stability theory applications, Automatica 42(4): 573–587.
- [9] Grünbaum, B. (2003). Convex Polytopes, 2nd Edn., Graduate Texts in Mathematics, Vol. 221, Springer-Verlag, New York, NY.
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- [11] Haddad, W.M., Chellaboina, V. and Nersesov, S.G. (2006). Impulsive and Hybrid Dynamical Systems, Princeton Series in Applied Mathematics, Princeton University Press, Princeton, NJ.
- [12] Heemels, W.P.M.H., De Schutter, B. and Bemporad, A. (2001). Equivalence of hybrid dynamical models, Automatica 37(7): 1085–1091.
- [13] Hudson, J.F.P. (1969). Piecewise Linear Topology, University of Chicago Lecture Notes, W.A. Benjamin, Inc., New York, NY/Amsterdam.
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- [16] Lang, S. (1999). Fundamentals of Differential Geometry, Graduate Texts in Mathematics, Vol. 191, Springer-Verlag, New York, NY.
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- [18] Leth, J. and Wisniewski, R. (2012). On formalism and stability of switched systems, Journal of Control Theory and Applications 10(2): 176–183.
- [19] Liberzon, D. (2003). Switching in Systems and Control, Systems & Control: Foundations & Applications, Birkhäuser, Boston, MA.
- [20] Lygeros, J., Johansson, K.H., Simić, S.N., Zhang, J. and Sastry, S.S. (2003). Dynamical properties of hybrid automata, IEEE Transactions on Automatic Control 48(1): 2–17.
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- [24] Rienmüller, T., Hofbaur, M., Travé-Massuyès, L. and Bayoudh, M. (2013). Mode set focused hybrid estimation, International Journal of Applied Mathematics and Computer Science 23(1): 131–144, DOI: 10.2478/amcs-2013-0011.
- [25] Simić, S.N., Johansson, K.H., Lygeros, J. and Sastry, S. (2005). Towards a geometric theory of hybrid systems, Dynamics of Continuous, Discrete & Impulsive Systems B: Applications & Algorithms 12(5–6): 649–687.
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- [29] van der Schaft, A. and Schumacher, H. (2000). An Introduction to Hybrid Dynamical Systems, Lecture Notes in Control and Information Sciences, Vol. 251, Springer-Verlag, London.
- [30] Wisniewski, R. (2006). Towards modelling of hybrid systems, 45th IEEE Conference on Decision and Control, San Diego, CA, USA, pp. 911–916.
- [31] Wisniewski, R. and Leth, J. (2011). Convenient model for systems with hystereses-control, Proceedings of the 50th IEEE Conference on Decision and Control, Orlando, FL, USA.
- [32] Yang, H., Jiang, B., Cocquempot, V. and Chen, M. (2013). Spacecraft formation stabilization and fault tolerance: A state-varying switched system approach, System & Control Letters 62(9): 715–722.
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Typ dokumentu
Bibliografia
Identyfikator YADDA
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