New LMI formulation for control design of discrete linear repetitive system

This paper addresses the stability analysis along the pass and the synthesis problem of linear 2D/repetitive systems (i.e. information propagation in two independent directions). A new sufficient condition for the synthesis problem in the case of MIMO is also given for both discrete repetitive linear. A necessary and sufficient condition for analysis and synthesis for discrete repetitive linear MISO systems is presented. These new results are expressed in term of LMI (linear matrix inequalities). Numerical examples are provided to illustrate the effectiveness of the proposed formulations.