Abstract : In this chapter, we study the delay effects in visual tracking problems for an optronic sighting system. We first describe the physical model and then give a simplified version defined by an integrator and a time-delay. We then state the visual tracking problems that are considered. To solve these problems, we first have to study the stabilization problem for the system defined above. Since this problem is a particular case of the general problem of parametrizing all the stabilizing controllers of a stable perturbation of a (infinite-dimensional) stabilizable plant, this problem is studied in its generality. Within the fractional representation approach to synthesis problems, we give an elementary proof for the existence of a general parametrization of all the stabilizing controllers of a stabilizable plant which does not necessarily admit doubly coprime factorizations. Only the knowledge of a (finite-dimensional) stabilizing controller is required. If the plant admits doubly coprime factorizations, then this parametrization yields the Youla-Kučera parametrization. Finally, using the above results, we study the tracking problems and show numerical simulations in which our results are compared with a PID and a H∞ -controller.
