Abstract
Sylvester equations, their duals, and their nonlinear generalizations arise in a wide variety of systems and control problems. Here we provide an overview of classical and recent applications of these equations in output regulation, stabilization of cascaded systems, observer design, and model order reduction, for both linear and nonlinear systems. Similarities and differences between the linear and nonlinear cases are highlighted, with an emphasis on how design formulations and associated dual designs for linear systems may generalize to the nonlinear setting.
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