Nonlinear rational approximation using generalized orthonormal basis

Nonlinear rational approximation is discussed by solving a Nehari type approximation problem when the system transfer function is modeled by weighted partial sums of generalized orthonormal expansions. Two solutions are presented, the first is carried out in a state space framework and the second follows a more direct approach, transforming the original problem to an H^∞ optimization problem. The orthonormal basis is generated by finite Blaschke products specified by the pole locations of the system. This makes possible to incorporate a priori knowledge about flexible structures obtaining a low order representation of the system.