Structural Engineering and Mechanics

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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)
  • Received : 2010.12.08
  • Accepted : 2012.01.03
  • Published : 2012.01.25
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Abstract

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.

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