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Estimation of attraction domain of nonlinear systems with saturated impulses and input disturbances

In this article, the estimation of attraction domain of nonlinear systems with saturated impulses and input disturbances is investigated. The sufficient conditions which can ensure the robust convergence of a class of nonlinear dynamical systems for every initial condition in the attraction domain are established. Moreover, some optimization problems are proposed to design the control gain so as to enlarge the size of the estimation of attraction domain as much as possible with a prespecified decay rate. In addition, the exponential stabilization and the estimation of attraction domain for nonlinear dynamical systems under this saturated impulsive control without disturbances are also studied. Finally, simulation results for a chaotic oscillator are displayed to show the effectiveness and feasibility of our results.