Generalized â„‹2 model approximation for differential linear repetitive processes

This paper investigates the generalized â„‹2 model approximation for differential linear repetitive processes (LRPs). For a given LRP, which is assumed to be stable along the pass, we are aimed at constructing a reduced-order model of the LRP such that the generalized â„‹2 gain of the approximation error LRP between the original LRP and the reduced-order one is less than a prescribed scalar. A sufficient condition to characterize the bound of the generalized â„‹2 gain of the approximation error LRP is presented in terms of linear matrix inequalities (LMIs). Two different approaches are proposed to solve the considered generalized â„‹2 model approximation problem. One is the convex linearization approach, which casts the model approximation into a convex optimization problem, while the other is the projection approach, which casts the model approximation into a sequential minimization problem subject to LMI constraints by employing the cone complementary linearization algorithm. A numerical example is provided to demonstrate the proposed theories.