LMIs in Control/Click here to continue/Applications of Linear systems/An LMI based static output feedback control to design a flight control system

An LMI based static output feedback control to design a flight control system for UAV's

Introduction
Since UAV's can perform various dangerous tasks which do not require the intervention of human beings, the robust control design of UAV's has been extensively worked on during the past years. The main advantage of implementing Static Output Feedback control design to UAV's is that it requires only the internal signals available in the plant for control purpose.

System Representation
The state space representation of the Linear time invariant system

$$ \begin{align} \dot{x}(t) &= Ax(t) + Bu(t) + B_v v(t)\\ \end{align} $$

$$ \begin{align} y(t) = Cx(t) \end{align} $$

Control Law
$$ \begin{align} u(t) = -Ky(t) = -KCx(t) \end{align} $$

The LMI
$$ \begin{align} \begin{bmatrix} P_nA_i+A_i^TP_n+Q & P_nB_i & P_nB_vi & L_n^T\\ B_i^T P & -R & 0 & 0\\ B_vi^T P & 0 & -\gamma^2I & 0\\ L_n & 0 & 0 & -R\\ \end{bmatrix} <= 0 \end{align} $$

Conclusions
The approach proposed above can be used for nominal and perturbed models.