Finite dimensional approximations of unstable infinite dimensional systems

The approximation of possibly unstable linear infinite-dimensional systems is studied. The system transfer function is assumed to be continuous on the imaginary axis with finitely many poles in the open right half plane. A unified approach is proposed for rational approximations of such infinite-dimensional systems. Under a certain mild frequency domain condition, a procedure is developed for constructing a sequence of finite-dimensional approximants which converges to the true model in the L_∞ norm. It is noted that the proposed technique uses only the fast Fourier transform and the singular value decomposition algorithms for obtaining the approximations. Some examples are included to illustrate the proposed method