FINITE-ELEMENT APPROXIMATIONS OF COMPENSATOR DESIGN FOR ANALYTIC GENERATORS WITH FULLY UNBOUNDED CONTROLS OBSERVATIONS

An approximation theory leading to a design of a finite-dimensional co mpensator for control systems generated by analytic semigroups is pres ented. The novelty of this paper with respect to other results availab le in the literature is threefold: (i) it treats fully unbounded contr ol/observation operators; (ii) it does not require compactness propert y of the underlined generator (an assumption that is often violated in practice); and (iii) the design of a finite-dimensional compensator i s based on finite element approximation of the original model rather t han on modal (eigenfunctions) approximations which, in turn, require t he a priori knowledge of the eigenvalues for the system. Applications of the theory to heat equations and plate equations are provided.