Computation and stability of limit cycles in hybrid systems

Autor: J.P. Louis, Pierre Riedinger, D. Flieller
Přispěvatelé: Riedinger, Pierre, Groupe de Recherche en Electrotechnique et Electronique de Nancy (GREEN), Université de Lorraine (UL), Centre de Recherche en Automatique de Nancy (CRAN), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Systèmes et Applications des Technologies de l'Information et de l'Energie (SATIE), École normale supérieure - Cachan (ENS Cachan)-Université Paris-Sud - Paris 11 (UP11)-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-École normale supérieure - Rennes (ENS Rennes)-Université de Cergy Pontoise (UCP), Université Paris-Seine-Université Paris-Seine-Conservatoire National des Arts et Métiers [CNAM] (CNAM)-Centre National de la Recherche Scientifique (CNRS)
Jazyk: angličtina
Rok vydání: 2006
Předmět:
0209 industrial biotechnology
Hybrid systems
Computation
Stability (learning theory)
Context (language use)
02 engineering and technology
[PHYS.COND.CM-S] Physics [physics]/Condensed Matter [cond-mat]/Superconductivity [cond-mat.supr-con]
01 natural sciences
[SPI.AUTO]Engineering Sciences [physics]/Automatic
symbols.namesake
020901 industrial engineering & automation
sensitivity analysis
Control theory
Limit cycle
0103 physical sciences
Sensitivity (control systems)
Limit (mathematics)
010301 acoustics
Mathematics
Applied Mathematics
[SPI.ELEC] Engineering Sciences [physics]/Electromagnetism
[SPI.NRJ]Engineering Sciences [physics]/Electric power
[PHYS.COND.CM-S]Physics [physics]/Condensed Matter [cond-mat]/Superconductivity [cond-mat.supr-con]
[SPI.ELEC]Engineering Sciences [physics]/Electromagnetism
[SPI.AUTO] Engineering Sciences [physics]/Automatic
Hybrid system
Jacobian matrix and determinant
symbols
Analysis
[SPI.NRJ] Engineering Sciences [physics]/Electric power
Zdroj: Nonlinear Analysis: Theory, Methods and Applications
Nonlinear Analysis: Theory, Methods and Applications, Elsevier, 2006, 64 (2), pp.352-367
ISSN: 0362-546X
Popis: International audience; In this note, a practical way to compute limit cycles in context of hybrid systems is investigated. As in many hybrid applications the steady state is depicted by a limit cycle, control design and stability analysis of such hybrid systems require the knowledge of this periodic motion. Analytical expression of this cycle is generally an impossible task due to the complexity of the dynamic. A fast algorithm is proposed and used to determine these cycles in the case where the switching sequence is known. The proposed method is based on the rule played by the switching times in the sensitivity functions. The stability of the cycle is also deduced at the end of the run thanks to the computation of the Jacobian matrix of the linearized sampled time systems. This work can be used as a starting point for sensibility analysis, measurement of attraction area and control design.
Databáze: OpenAIRE
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