Finite-dimensional approximation and error bounds for spectral systems with partially known eigenstructure

An approach is presented for directly computing bounds on the frequency-response error between finite-dimensional modal models and the full infinite-dimensional models of systems described by certain classes of linear hyperbolic and parabolic partial differential equations (PDE's). The models and bounding techniques are developed specifically to be computable when applied to hyperbolic and parabolic systems with spatially variant parameters, complicated boundary shapes, and other cases where the eigenstructure is not available in closed form and must be computed numerically. A controller design example is presented to illustrate the utility of this approach