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.