This paper investigates the global stabilization for a class of high-order time-delay nonlinear systems. Compared with the existing references, a distinct characteristic of this paper rests in time-delay entering high-order, low-order, and linear growth parts of system nonlinearities. Based on Lyapunov-Krasovskii theorem and necessary improvement of the adding a power integrator method, a continuous global state-feedback controller is constructed to preserve the equilibrium at the origin and guarantees the global asymptotic stability of the resulting closed-loop system. Finally, a simple example is provided to demonstrate the validness of the proposed approach.
This paper is concerned with adaptive stabilization for a class of uncertain high-order nonlinear systems with time delays. To the authors' knowledge, there has been no analogous result. Hence during investigation, the conditions on delay effect and the control design framework should be established for the first time. In this paper, under somewhat necessary restrictions on the system nonlinearities, by the method of adding a power integrator and the related adaptive technique, a procedure is developed to design the continuous adaptive state-feedback controller without overparametrization. Moreover, the uniform stability and convergence of the resulting closed-loop system are rigorously proven, with the aid of a suitable Lyapunov-Krasovskii functional. Finally, a numerical example is provided to illustrate the effectiveness of the theoretical result.
SummaryThis article designs an adaptive event‐triggered controller to solve the problem of global finite‐time stabilization for a class of uncertain nonlinear systems. By using the symbol function technique, the event‐triggered error is completely compensated, the adaptive technique and the back‐stepping method are simultaneously applied to the controller design, and the new way of designing controller is completed on the basis of fast finite‐time stability theory. Subsequently, taking Lyapunov stability theorem into account, the system stability is proved, and the system is demonstrated by contradiction to be non‐zeno. Finally, giving a simulation example to display the feasibility of this method.
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