On the design and the digital implementation of observer‐based controllers for tracking of nonlinear time‐delay systems

In this article, the tracking control problem for a class of nonlinear time‐delay systems is investigated. In particular, a new methodology for the design and the digital implementation of observer‐based tracking controllers is provided for a class of control‐affine nonlinear systems with state delays. First, a procedure for the design of continuous‐time observer‐based tracking controllers ensuring the global asymptotic stability of the corresponding closed‐loop tracking error system is provided for the considered class of systems. Then, sufficient conditions are provided for the existence of a suitably fast sampling and of an accurate quantization of the input/output channels such that the digital implementation of the proposed continuous‐time observer‐based tracking controller ensures the semi‐global practical stability property of the related sampled‐data quantized closed‐loop tracking error system, with arbitrarily small final target ball of the origin. Moreover, it is shown that, in the special case of delay‐free nonlinear systems, the sufficient conditions provided for the digital implementation of the proposed continuous‐time observer‐based tracking controller can be strongly relaxed. In the theory here developed, time‐varying sampling periods and nonuniform quantization of the input/output channels are taken into account. The proposed results are validated through examples concerning a class of neural networks systems and a class of time‐delay systems including, as a special case, a delay‐free actuated inverted pendulum.