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Estimation of Region of Attraction for Polynomial Nonlinear Systems

This post is an excerpt from the journal ISA Transactions.  All ISA Transactions articles are free to ISA members, or can be purchased from Elsevier Press.

Abstract: This paper introduces a numerical method to estimate the region of attraction for polynomial nonlinear systems using sum of squares programming. This method computes aControl Room local Lyapunov function and an invariant set around a locally asymptotically stable equilibrium point. The invariant set is an estimation of the region of attraction for the equilibrium point. In order to enlarge the estimation, a subset of the invariant set defined by a shape factor is enlarged by solving a sum of squares optimization problem. In this paper, a new algorithm is proposed to select the shape factor based on the linearized dynamic model of the system. The shape factor is updated in each iteration using the computed local Lyapunov function from the previous iteration. The efficiency of the proposed method is shown by a few numerical examples.

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2006 Elsevier Science Ltd. All rights reserved.

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