Robust robust model reduction

The problem of linear model reduction is addressed. Given a state-space model of a linear time-invariant system, a model of prescribed order is obtained such that the H₂-norm of the difference between the transference of the two models is minimized. The reduced model is modeled as having the same order as the system but with a nonminimal observer form realization. The solution is then based on full order LMIs. The model reduction method is extended to the case where the model to be reduced suffers from parameters uncertainties that lie in a prescribed polytope. A reduced order model is obtained that achieves a prescribed upper-bound on the H₂-norm of the differences between the transference of the reduced order model and all the transferences of all the possible systems in the polytope.