  Linear Quadratic Regulator (LQR) design is one of the most classical optimal
control problems, whose well-known solution is an input sequence expressed as a
state-feedback. In this work, finite-horizon and discrete-time LQR is solved
under stability constraints and uncertain system dynamics. The resulting
feedback controller balances cost value and closed-loop stability. Robustness
of the solution is modeled using the scenario approach, without requiring any
probabilistic description of the uncertainty in the system matrices. The new
methods are tested and compared on the Leslie growth model, where we control
population size while minimizing a suitable finite-horizon cost function.
