Model reduction via tangential interpolation

with input u(t) ∈ Rm, state x(t) ∈ RN and output y(t) ∈ Rp. Without loss of generality, we can assume that the system is controllable and observable since otherwise we can always find a smaller dimensional model that is controllable and observable, and that has exactly the same transfer function. In addition to this, we will assume that the system is stable, i.e. the generalized eigenvalues of the pencil sE − A lie in the open left half plane (this also implies that E is non-singular). When the system order N is too large for solving various control problems within a reasonable computing time, it is natural to consider approximating it by a reduced order system { Ê ̇̂ x = Âx̂ + B̂u ŷ = Ĉx̂ + D̂u (2)