H<sub>∞</sub> Control of 2-D State-Delayed Systems with Uncertainties

Abstract

This paper studies robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control problem for 2D discrete systems with state delays. Firstly, H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance of 2D discrete state-delayed systems in local state-space (LSS) Fornasini-Marchesini (FM) second model is considered. The definition of H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance is proposed and based on it, we obtain the sufficient conditions described by RDI and LMI, respectively, i.e. bounded real lemma, which assure the stability and H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance of 2D state-delayed systems. Then we design a state feedback controller applying the LMI condition, which makes 2D uncertain state-delayed system have H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance Υ. Moreover, an optimization problem is proposed to guarantee the minimum H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> norm bound Υ and the according controller can be obtained. Finally, a numerical example is given to demonstrate the effectiveness of our results.