کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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1137255 | 1489167 | 2010 | 12 صفحه PDF | دانلود رایگان |
In this paper a methodology for the estimation of domains of attraction of stable equilibriums based on maximal Lyapunov functions is proposed. The basic idea consists in finding the best level set of a Lyapunov function which is fully contained in the region of negative definiteness of its time derivative. An optimization problem is formulated, which includes a tangency requirement between the level sets and constraints on the sign of the numerator and denominator of the Lyapunov function. Such constraints help in avoiding a large number of potential dummy solutions of the nonlinear optimization model. Moreover, since global optimality is also required for proper estimation, a deterministic global optimization solver of the branch and bound type is adopted. The methodology is applied to several examples to illustrate different aspects of the approach.
Journal: Mathematical and Computer Modelling - Volume 52, Issues 3–4, August 2010, Pages 574–585