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Convergence analysis of nonlinear dynamical systems by nested Lyapunov functions

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2 Author(s)
Peterfreund, N. ; Center for Eng. Syst. Adv. Res., Oak Ridge Nat. Lab., TN, USA ; Baram, Y.

A method for estimating the domain of attraction of an asymptotically stable equilibrium point of a nonlinear dynamical system and for deriving an upper bound on the time of convergence in the estimated domain is presented. It is based on a set of Lyapunov functions. Defined on nested regions in the state space. The estimated domain, obtained as the union of a subset of these regions, is based on a local Lyapunov-like condition for the convergence of the solution in each region to its inner boundary. A bound on the time of convergence within the estimated domain is given by the sum of the local bounds. This concept is implemented using a class of regions whose boundaries are described by Fourier series

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Automatic Control, IEEE Transactions on  (Volume:43 ,  Issue: 8 )