  The design of direct data-based controllers has become a fundamental part of
control theory research in the last few years. In this paper, we consider three
classes of data-based state feedback control problems for linear systems. These
control problems are such that, besides stabilization, some additional
performance requirements must be satisfied. First, we formulate and solve a
trajectory-reference control problem, on which desired closed-loop trajectories
are known and a controller that allows the system to closely follow those
trajectories is computed. Then, in the area of data-based optimal control, we
solve two different problems: the inverse problem of optimal control, and the
solution of the LQR problem for continuous-time systems. Finally, we consider
the case in which the precise position of the desired poles of the closed-loop
system is known, and introduce a data-based variant of a robust pole-placement
procedure. Although we focus on continuous-time systems, all of the presented
methods can also be easily formulated for the discrete-time case. The
applicability of the proposed methods is tested using numerical simulations.
