On H∞ model reduction for discrete-time systems using LMIs and bilinear transformation

For discrete-time LTI systems, we extended the LMIs-based continuous-time H_∞ model reduction problems via bilinear transformation, and obtained an equivalent proposition of the discrete-time γ-suboptimal H_∞ model reduction. In addition, the bounds of H_∞ cost were given, thus the infimum of which was gained. Finally, given the constraints and computer implementation of MATLAB-LMI, an algorithm which can construct discrete-time H_∞ optimal reduced-order model was proposed.