A result on stability of one-state nonlinear dynamical systems

A simple method for determining an estimate of the domain of attraction for the state-space origin is presented for the class of one-state nonlinear dynamical systems. The solution is obtained on the basis of a simple determinantal criterion, which points out when a matrix depending on a parameter loses its definiteness and allows one to derive easily the desired region in the state-space. The proposed method applies to feedback systems with a generic scalar nonlinearity, thus permitting a wide range of applications. The computational complexity is low.<
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