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Further Results on Output Tracking for a Class of Uncertain High-Order Nonlinear Time-Delay Systems DOI:10.15199/48.2019.05.22

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The control design is one of the most relevant topics in nonlinear system theory, so a number of researchers have paid particular attention to it, for example, it can be seen in references [1-11]. The fundamental problem is to construct a feedback control law making the controlled output track a given reference signal as much as possible. The problem of global practical tracking for nonlinear state feedback systems was solved by the method of adding a power integrator [3,4] and using the idea of universal control [1,2]. However, the above results do not take into account time delays and their impact on the system as a whole. For example, in three-dimensional systems, delay is determined by the fact that the signals propagate at a finite speed and they need time to overcome distances [12]. Delay of the reaction to the signal and feedback with delay are inherent in many physical [13], chemical [14], climatic [15] and biological [16] objects and processes. In the study of systems with delay, it is important to know the values of time delays, the value of which largely determines the dynamics and properties of the system. Since time-delay exists widely in many practical systems such as electrical networks, microwave oscillator, and hydraulic systems, etc., and usually makes the considered system instable, to achieve some control objectives such as stabilization and trajectory tracking, the influence of time delay phenomenon should be considered. In view of these facts, it is meaningful and necessary to study control problems of accidental nonlinear systems with unknown parameters and time-delays. In recent years, by employing the Lyapunov-Krasovskii method to deal with the time-delay, control theory, and techniques for stabilization problem of time-delay nonlinear systems were greatly developed and advanced methods have been made; see, for instance, [17-21] and reference therein. Compared with study the stabilization problem [...]

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