On the design of finite-dimensional stabilizing compensators for infinite-dimensional feedback-systems via semiinfinite optimization

The computational stability criterion presented by E. Polak and T.L. Wuu (see ibid., vol.34, p.196-200, Feb. 1989) is extended to a form that can be used in the design of finite-dimensional stabilizing compensators for a class of feedback systems with infinite-dimensional plants. Since, in this case, the characteristic function is not a polynomial, there is no simple way to define a normalizing polynomial. Hence, approximation theory has to be used. The new stability test guarantees not only input-output stability, but also internal stability of the feedback system. Furthermore, since the numerical implementation of the test does not depend on the use of a reduced plant model, the test does not lead to spillover effects. Because the compensator is parametrized in the state-space form, the order of the compensator can be assigned by the designer