Robust ℋ2 model matching from frequency domain specifications

Abstract

This study addresses the problem of designing compensators for robust model matching. Firstly, the open-loop reference model (obtained, for instance, from classical frequency domain specifications), Gm(s), is recast as the product between two transfer functions GR(s) and Gr(s). A robust state feedback control law is synthesised such that an upper-bound on the ℋ2-norm of the error system between the uncertain system and Gr(s) is minimised, where the state feedback gain is determined through a convex optimisation problem over linear matrix inequality constraints. In addition, block GR(s) behaves as a series compensator in a unity feedback strategy aiming a robust steady state performance. A robust observer scheme is also proposed whenever the states are not available online to the state feedback controller. Numerical examples are presented to illustrate the approach.