Finite dimensional approximation and robust controller design for semigroup systems

It is shown that the doubly Bezout factorizations of a constructed approximation converge to those of the semigroup systems correspondingly. The feedbacks and output injections designed according to the finite dimensional approximations are shown to be able to stabilize the semigroup systems. It is found that the unstable parts of the approximating systems are identical to those of the semigroup systems when the dimensions are sufficiently high. It is revealed that the largest robust stability radius is continuous on the space of finite dimensional systems with the gap topology