Abstract
A technique of gradual approximation of the domain of attraction in the case of nonlinear continuous and discrete analytical dynamical systems is presented. The technique is based on the gradual extension of the “embryo” of the optimal Lyapunov function and gives, at each step, a new, open and non-empty piece of the domain of attraction. For a nonlinear dynamical system with control, defined by an analytical autonomous system of differential equations or difference equations, using domains of attraction, it is shown that two steady states, which belong to an analytic path of asymptotically stable steady states, can be transferred gradually one in the other by successive changes of the values of the control parameters. Numerical examples are given for the ALFLEX reentry vehicle and for a discrete dynamical system considered recently in the literature.
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