A finite dimensional modeling with explicit error bounds for spectral systems

In this paper, we present a reduced order modeling technique for a stable self-adjoint spectral system with unbounded input/output operators. An uncertainty model which covers the original distributed parameter system is formulated in view of finite dimensional controller design using linear robust control theory. The model is made of a finite dimensional nominal plant and frequency domain additive error bounds. The nominal model is a modal truncation containing a feed-through term with no dc errors between the nominal plant and the system. The bound is computable using elements of the system and partial knowledge of spectral structure. The formula obtained can be readily applicable to a wide class of systems including heat conduction and diffusion, and easily extended for systems with vibration