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Using impulses to control the convergence toward invariant surfaces of continuous dynamical systems

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  • Marão, José
  • Liu, Xinzhi
  • Figueiredo, Annibal

Abstract

Let us consider a smooth invariant surface S of a given ordinary differential equations system. In this work we develop an impulsive control method in order to assure that the trajectories of the controlled system converge toward the surface S. The method approach is based on a property of a certain class of invariant surfaces whose the dynamics associated to their transverse directions can be described by a non-autonomous linear system. This fact allows to define an impulsive system which drives the trajectories toward the surface S. Also, we set up a definition of local stability exponents which can be associated to such kind of invariant surface.

Suggested Citation

  • Marão, José & Liu, Xinzhi & Figueiredo, Annibal, 2012. "Using impulses to control the convergence toward invariant surfaces of continuous dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 45(8), pages 1067-1079.
    • Handle: RePEc:eee:chsofr:v:45:y:2012:i:8:p:1067-1079
    DOI: 10.1016/j.chaos.2012.05.002
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    References listed on IDEAS

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    1. Figueiredo, Annibal & Rocha Filho, Tarcisio M., 2009. "Basins of attraction of invariant regular manifolds," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1877-1889.
    2. Chen, Dilan & Sun, Jitao & Huang, Changshui, 2006. "Impulsive control and synchronization of general chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 213-218.
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    Cited by:

    1. Yang, Xueyan & Peng, Dongxue & Lv, Xiaoxiao & Li, Xiaodi, 2019. "Recent progress in impulsive control systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 244-268.

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