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

AbstractThis 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.Keywords: high-order time-delay nonlinear systemsglobal stabilisationadding a power integratorLyapunov–Krasovskii functionalsign functions AcknowledgementsThe authors would like to express sincere gratitude to the editor Prof. Lamnabhi-Lagarrigue and the referees for their valuable comments in improving the quality and the presentation of the paper. This study was supported by National Natural Science Foundation of China (61004013, 1273125, 61203013), the Shandong Provincial Natural Science Foundation of China (ZR2010FQ003, ZR2012FM018), the Specialised Research Fund for the Doctoral Program of Higher Education (20103705110002, 20113705120003), the Outstanding Middle-Age and Young Scientist Award Foundation of Shandong Province (BS2011DX012), the Project of Taishan Scholar of Shandong Province and the Doctoral Scientific Research Start-Up Foundation of Qufu Normal University.Notes++