Digital Control of Distributed Parameter Systems: A State-Space Approach

摘要

Two modern discrete-time control theories represent the theoretical framework forthis thesis where we have approached the problem of digital control of infinite-dimensional systems with possible unbounded input and/or output operators. We have outlined the main Popov theory based results on the discrete-time H-infinity control problem and we have given a full extension to discrete-time infinite-systems of the classical results of discrete Hyland-Bernstein theory known in the literature. Having available the framework offered by these two discrete control theories, we have approached the problem of digital control of linear infinite-dimensional systems with unbounded input and/or output operators. The type of unboundedness considered here was the one commonly accepted for systems that fall in the so-called Pritchard-Salamon class. Another feature that has been captured in the picture offered by this dissertation is represented by the fact that the two discrete control theories we have applied are suitable for coping with so-called singular control problems. The last part of this thesis was concerned with the applications. Two special Pritchard-Salamon systems, a parabolic system and a hyperbolic one were considered.