This paper is devoted to work out a stabilized controller by state feedback for a class of nonlinear systems. In this paper, we not only extend the existing results that system has a single power term to the case with multiple coupling power terms, but also consider that the power is time varying, which makes the system studied in this paper more general than that in other literature. By the backstepping method, a linear easy-to-implement controller is designed, which not only ensures the stability of the system but also has a good convergence speed. Finally, with a representative numerical example, by calculating all the parameters in the design procedure, the simulation shows that all the responses of the states and the controller are asymptotically stable at the equilibrium zero, which verifies the effectiveness of the control design scheme of this paper.

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This paper is devoted to the research of adaptive command filter tracking control for a class of uncertain nonlinear systems. The coexistence of multiple high-order coupling terms, unknown coefficients of time-varying function and uncertain external disturbances makes the studied system essentially different from the existing results. By skillfully combining adaptive technology, command filter control and backstepping method, a new type of adaptive command filter tracking control algorithm is designed. This controller not only solves the problem of complex explosion, but also introduces compensation signals to achieve higher precision tracking effect. Ultimately, the validity of the control algorithm is verified by numerical simulation and practical application model simulation experiments.