\subsection{Simple model}
% picture of UAV
The UAV model has been already analyzed --cite Tomas--. Thanks to symmetrical body of the UAV, both axis have the same model. For one axis, the states take form of
$\vec{x}_x = (x_x; \dot{x}_x; \ddot{x}_x)^T$ and $\vec{x}_y = (x_y; \dot{x}_y; \ddot{x}_y)^T$, where $x_x$ is the aileron and $x_y$ is the elevator position. The system in discrete state space model takes form of system matrices $\textbf{A}_s, \textbf{B}_s$ according to equation \ref{eq:state_space_model}