Infinite-dimensional Sylvester equation in observers design

This paper studies the infinite-dimensional algebraic Sylvester equation and its application to the problem of designing an asymptotic observer for a linear infinite-dimensional system with bounded input and unbounded output operators. The main general results on the infinite-dimensional differential and algebraic Sylvester equations are derived by employing the concept of an implemented semigroup (see [5], [6], [8]). Then the results are shown to be useful in the design of asymptotic infinite-dimensional observers.