On the Dynamical Systems Stability Control and Applications

Abstract:

The stability control analyzed by us, in this show, is based on our results in the domain of dynamical systems that depend of parameters. Any dynamical system can be considered as dynamical system that depends of parameters, without numerical particularization of them. All concrete dynamical systems, meted in the specialized literature, underline the property of separation between the stable and unstable zones, in sense of Liapunov, for two free parameters. This property can be also seen for one or more free parameters. Some mathematical conditions of separation between stable and unstable zones for linear dynamical systems are identified by us. For nonlinear systems, the conditions of separation may be identified using the linear system of first approximation attached to nonlinear system. A necessary condition of separation between stable and unstable zones, identified by us, is the sufficient order of differentiability or conditions of continuity for the functions that define the dynamical system. The property of stability zones separation can be used in defining the strategy of stability assurance and optimizing of the parameters, in the manner developed in the paper. The cases of dynamical systems that assure the separations of the stable and unstable zones, in your evolution, and permit the stability control, are analyzed in the paper.

• Periodical: Applied Mechanics and Materials (Volume 555)
• Pages: 361-368
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.555.361
• Online since: June 2014
• Authors: Marcel Migdalovici*, Daniela Baran, Gabriela Vlădeanu
• Keywords: Dynamical System, Stability Control, Stability Zones Separation

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