Szukana fraza: [Abstract = But it is just systems and control theory where Sylvester equations widely appear, and for this reason we intend to give a mathematically rigorous introduction to the subject which is tailored to researchers and postgraduate students working on systems and control. This goal motivates the assumptions under which the results are developed. As an important example of applications we study the problem of designing an asymptotic state observer for a linear infinitedimensional control system with a bounded input operator and an unbounded output operator.]

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