Computation of subsets of the domain of attraction for polynomial systems

In this paper the asymptotic stability of polynomial nonlinear systems is investigated. Our aim is to determine a region in the state space, which is a subset of the domain of attraction. We use the Lyapunov stability theory and the theorem of Ehlich and Zeller to achieve this aim. The inequality conditions given by the theorem of Ehlich and Zeller enable us to calculate inner and outer approximations to the relevant region of attraction. Two nontrivial examples conclude the paper and show the effectiveness of the presented method.

[1]  A. Levin.  An analytical method of estimating the domain of attraction for polynomial differential equations , 1994, IEEE Trans. Autom. Control..

[2]  B. Tibken.  Estimation of the domain of attraction for polynomial systems via LMIs , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[3]  Jean B. Lasserre,et al.  Global Optimization with Polynomials and the Problem of Moments , 2000, SIAM J. Optim..

[4]  O. Hachicho,et al.  Estimating domains of attraction of a class of nonlinear dynamical systems with LMI methods based on the theory of moments , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[5]  J. Thorp,et al.  Stability regions of nonlinear dynamical systems: a constructive methodology , 1989 .

[6]  Graziano Chesi,et al.  Computing optimal quadratic lyapunov functions for polynomial nonlinear systems via lmis , 2002 .

[7]  B. Tibken,et al.  Estimation of the domain of attraction for polynomial systems , 2005, The Fourth International Workshop on Multidimensional Systems, 2005. NDS 2005..

[8]  Karl Zeller,et al.  Schwankung von Polynomen zwischen Gitterpunkten , 1964 .

[9]  E. Davison,et al.  A computational method for determining quadratic lyapunov functions for non-linear systems , 1971 .

[10]  Alberto Tesi,et al.  On the stability domain estimation via a quadratic Lyapunov function: convexity and optimality properties for polynomial systems , 1996, IEEE Trans. Autom. Control..