Continuous global stabilisation of high-order time-delay nonlinear systems++

Abstract

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.