Exponential stabilization of delay neutral systems under sampled-data control

This paper considers the exponential stabilization of delay systems of the neutral type via sampled-data control. The control input of the neutral system can present a delay, constant or variable. The sampling period is not necessarily constant. It is only assumed that the time between to successive sampling instants is bounded. Since the sampling effect (sampling and zero-holder) is equivalent to a variable delay, the resulting system is modelled as a continuous-time one, where the control input has a 'non-small' time-varying delay belonging to some interval [h - μ, h + μ]. For instance, h - μ may represent the minimum input delay, and 2μ the additional delay generated by the combination of the sampling effect with the input delay variation. This results in a system with 'non-small' time-varying delays (i.e. delays with a known and non-zero minimum value), the exponential stabilization of which is possible under LMI conditions. Two examples are provided. The first one deals with the sampled-data control of a neutral system. The second one considers the stabilization of a flexible rod with continuous, delayed control