A Non-Iterative LMI-Based Design of Static Output Feedback Control with $\mathcal{L}_{2}$ Gain Performance for Linear Systems

In this paper, we present a new LMI-based non-iterative design strategy for static output feedback controllers with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{L}_{2}$</tex> Gain Performance for linear systems. In our approach, on the basis of the well-known necessary and sufficient condition for the existence of the static output feedback control for linear systems, the non-iterative LMI-based design procedure for the proposed static output feedback controller is derived. In this paper, we show the LMI-based non-iterative design procedure for static output feedback controllers with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{L}_{2}$</tex> Gain Performance and the effectiveness of the proposed static output feedback control is presented through a simple illustrative example.