Power, inverse power and orthogonal iteration algorithms for determining the eigenstructure of operators on infinite-dimensional Hilbert spaces are developed. Convergence properties of the algorithms are established for certain classes of operators associated with the control of systems described by partial differential equations. A simple finite-difference method is applied to a particular operator to illustrate the utility of the algorithms.

An approach is presented for directly computing bounds on the frequency-response error between infinite dimensional modal models and the full infinite dimensional models of systems described by certain classes of linear hyperbolic and parabolic 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.

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An approach is presented for directly computing bounds on the frequencyresponse error between finite-dimensional modal models and the full infinitedimensional 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 case8 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.