Continuous global tracking of a class high-order time-delay nonlinear systems

Abstract

This paper deals with the problem of global practical tracking for a class of high-order nonlinear systems with time delay. The peculiarity of the system under study is that the degree of restriction on the upper limit of nonlinearity can be obtained in a continuous interval. By introducing a sign (signum) function and adding a generalized method for enabling the power integrator, as well as selecting the corresponding Lyapunov function, we create an adjustable and time-independent tracking controller that will dominate the time-delayed nonlinearity. All the closed system states obtained as a result of the developed controller are widely limited and ensure that the tracking error after the set time is sufficiently small. A numerical example is given to demonstrate the effectiveness and validity of the proposed design.