Structural Engineering and Mechanics

  • 제41권2호
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  • Pages.263-284
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  • 2012
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Estimating the Region of Attraction via collocation for autonomous nonlinear systems

  • Rezaiee-Pajand, M. (Department of Civil Engineering, Ferdowsi University of Mashhad) ;
  • Moghaddasie, B. (Department of Civil Engineering, Ferdowsi University of Mashhad)
  • 투고 : 2010.12.08
  • 심사 : 2012.01.03
  • 발행 : 2012.01.25
⟨ 이전 논문 다음 논문 ⟩

초록

This paper aims to propose a computational technique for estimating the region of attraction (RoA) for autonomous nonlinear systems. To achieve this, the collocation method is applied to approximate the Lyapunov function by satisfying the modified Zubov's partial differential equation around asymptotically stable equilibrium points. This method is formulated for n-scalar differential equations with two classes of basis functions. In order to show the efficiency of the suggested approach, some numerical examples are solved. Moreover, the estimated regions of attraction are compared with two similar methods. In most cases, the proposed scheme can estimate the region of attraction more efficient than the other techniques.

키워드

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피인용 문헌

  1. Review on computational methods for Lyapunov functions vol.20, pp.8, 2015, https://doi.org/10.3934/dcdsb.2015.20.2291
  2. Revised CPA method to compute Lyapunov functions for nonlinear systems vol.410, pp.1, 2014, https://doi.org/10.1016/j.jmaa.2013.08.014