Energy to peak (L₂-L∞) filtering for linear differential repetitive processes

Linear repetitive process is a special case of 2-D systems. Normally, in two time variables for the differential repetitive process, one is discrete and the other is differential, and the length of the differential variable is finite. For the problems of L₂-L∞, filtering for linear differential repetitive processes, a suitable filter is designed, and then a sufficient condition is given in terms of linear matrix inequality (LMI), which guarantees that the filtering error system is stable along the pass and has L₂-L∞, performance. Moreover, the solvability condition of desired filter is also established. All the conditions obtained in this paper are of the LMI form, which can be solved by using the standard software. A numerical example shows the effectiveness of the proposed design scheme.