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In this paper, we study the global output feedback stabilisation of a class of high-order nonlinear systems with more general low-order and high-order nonlinearities. By constructing the novel Lyapunov function and observer, based on the homogeneous domination theory together with adding a power integrator method, an output feedback controller is developed to guarantee the equilibrium of the closed-loop system globally uniformly asymptotically stable. [ABSTRACT FROM PUBLISHER]

This paper considers the finite-time stabilisation for a class of high-order nonlinear systems with both low-order and high-order nonlinearities. Based on the finite-time Lyapunov stability theorem together with the methods of dynamic gain control and adding one power integrator, a state feedback controller with gains being tuned online by two dynamic equations is proposed to guarantee the global finite-time stabilisation of the closed-loop system. [ABSTRACT FROM PUBLISHER]

This paper studies the state feedback control problem for a class of nonlinear systems with high-order and low-order nonlinearities. The introduction of the sign function together with the method of adding a power integrator and Lyapunov stability theorem makes the closed-loop system globally asymptotically stable. Exploiting the idea of how to deal with growth nonlinearities with both high order and low order being relaxed to some intervals is the focus of this work. [ABSTRACT FROM PUBLISHER]

Abstract: In this paper, by introducing a combined method of sign function, homogeneous domination and adding a power integrator, and overcoming several troublesome obstacles in the design and analysis, the problem of state feedback control for a class of nonlinear high-order feedforward systems with the nonlinearity's order being relaxed to an interval rather than a fixed point is solved. [Copyright &y& Elsevier]

This paper studies the global stabilisation problem for a class of high-order nonlinear systems with multiple time delays. A distinct property of the systems to be investigated is that powers on the upper bound restrictions of nonlinearities are allowed to take values on a continuous interval. By introducing the sign functions and using the generalised method of adding a power integrator, this paper successfully designs a continuous global state-feedback controller independent of time delays. Moreover, a novel Lyapunov–Krasovskii functional is constructed to prove the globally asymptotic stability of the resulting closed-loop system. [ABSTRACT FROM PUBLISHER]