Generalized ℋ₂ model approximation for differential linear repetitive processes

This paper investigates the generalized ℋ₂ 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 ℋ₂ 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 ℋ₂ 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 ℋ₂ 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.