Stabilization and regulation of infinite-dimensional systems using coprime factorizations

This paper surveys some of the results on stabilization and regulation of infinite-dimensional systems which have been obtained within the so-called fractional representation approach to feedback system analysis and synthesis. The relationship with state-space concepts is carefully discussed. The following topics are addressed: Rings of transfer functions and coprime factorizations, Pritchard-Salamon systems, External and internal closed-loop stability, Closed-loop stability and pole-zero cancellations, The Nyquist stability criterion, Closed-loop stability and the existence of coprime factorizations, Parametrization of all stabilizing controllers for a given plant, Existence of finite-dimensional stabilizing compensators, Strong stabilization by finite-dimensional controllers, The internal model principle, PI-control of uncertain infinite-dimensional systems.

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