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Continuous global stabilisation of high-order time-delay nonlinear systems. (English) Zbl 1278.93185

Summary: 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.

MSC:

93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93C10 Nonlinear systems in control theory
93D30 Lyapunov and storage functions
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