Techno Press
Techno Press

Structural Engineering and Mechanics   Volume 41, Number 2, January25 2012, pages 263-284
DOI: http://dx.doi.org/10.12989/sem.2012.41.2.263
 
Estimating the Region of Attraction via collocation for autonomous nonlinear systems
M. Rezaiee-Pajand and B. Moghaddasie

 
Abstract     [Full Text]
    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.
 
Key Words
    autonomous systems; Lyapunov function; Region of Attraction (RoA); modified Zubov\'s PDE; collocation method
 
Address
M. Rezaiee-Pajand and B. Moghaddasie: Department of Civil Engineering, Ferdowsi University of Mashhad, Mashhad 91175-1111, Iran
 

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