**10. Conclusions**

Often in complex digital control systems, for instance digital adaptive controllers in conjugation with complex dynamics with high degree of state interaction, the role played by the sampling time *h* is the algid point in the stability and control performance analysis. This is so because of the potential instability that may occur by improperly selected large *h*. This phenomenon is commonly magnified when a dead time is present. In any case, the appearance of perturbations and delays together in the dynamics makes the problem difficult to seize and comprehend.

An important example which meets these particularities is found in the control problem represented by the guidance of UUV´s in 6 DOF´s, which was taken here as case study.

**Author details**

Mario A. Jordan1,2,

Blanca, Argentina

**References**

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Jorge L. Bustamante1,2 and Carlos E. Berger1

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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

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

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 support of filtered data at any discrete time.

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 selected sufficiently small.
