ℓ∞-gain model reduction for discrete-time systems via LMIs

This paper deals with model order reduction for linear stable discrete-time systems while minimizing the lscr_infin-gain of the error system. Our approach considers explicitly time domain performance and not frequency domain performance like most other approaches do. A convex programming problem expressed in terms of linear matrix inequalities combined with a line search algorithm is formulated to provide suboptimal solutions to the model reduction problem. The proposed method is compared to the well-known balanced truncation method via simulation. It is shown that the proposed method results in superior performance when time domain performance is of importance.