Stabilization, tracking and disturbance rejection in linear multivariable distributed systems

The paper describes the algebra ß(σ0) of transfer functions of distributed systems; ß(σ0) generalizes the algebra of proper rational functions [see, e.g. 7,8]. The first theorem generalizes for the distributed case a result of Youla et al. [10]: any plant p can be stabilized by pre-or post-compensation and the closed-loop natural frequencies can be preassigned in Cσ 0+, the domain of definition of p. The second theorem generalizes for the distributed case the known results of the lumped case [for a detailed review, see 10]: stabilization and asymptotically zero tracking-error can be achieved by a precompensator with elements in ß (σ0). Furthermore, the stabilization and tracking is robust.