**Author details**

18 Advances in Discrete Time Systems

**Figure 2.** Evolution of the behaviour of a simulated UUV with adaptive control in all its modes.

support of filtered data at any discrete time.

selected sufficiently small.

Taking into consideration the hole of information caused by the presence of a pure delay in the adaptive control, we employs a filter for estimation of the actual state vector based on past measures together with a set of adaptive control matrices available over the delay period. The control end in the design is the minimization of certain incremental functional of the path energies of the geometric and kinematic errors. The control action can be then computed from predictions, as well as from the updating of the adaptive laws which succeeds with a

We relate the stability and control performance with certain sign non-definite terms that are present in the final incremental functional of energy. From therein it can be concluded about the existence of an attraction domain and a residual set. This last one is influenced in size by the local errors of predictions, the perturbations *δ* in the measurements and the pure discrete delay *d*. It was clearly shown, that the presence of *d* does affect exponentially in magnitude the size of the prediction errors, which may be critical for the control stability if *h* is not Mario A. Jordan1,2, Jorge L. Bustamante1,2 and Carlos E. Berger1

1 Instituto Argentino de Oceanografía IADO CCT-CONICET Bahía Blanca, Argentina 2 Universidad Nacional del Sur, Dto. de Ing. Eléctrica y de Computadoras UNS-DIEC, Bahía Blanca, Argentina
