  The aim of this work is to design controllers through explicit minimization
of the settling time of a closed-loop response, by using a class of methods
adequate for this objective. To the best of our knowledge, all the methods
available in the literature do not minimize directly the settling time but only
related objective functions. Indeed, the settling time objective function is
not only non-smooth but also discontinuous. Therefore we propose to use direct
search methods, which do not use any gradient information. An important reason
is a recent result that some direct search methods are guaranteed to
convergence on such discontinuous objective functions. The proposed approach is
self-standing but can also improve the solutions obtained with the alternatives
of the literature, which lead to good solutions but suboptimal in terms of the
settling time. Note also that this approach is very flexible and can be adapted
to a broad range of objectives as well as nonlinear systems or controllers, as
long as the time response can be simulated.
