A bilinear formulation for the output feedback problem in linear systems

This note ties together a geometric theory and previous algebraic results for the closed-loop eigenstructure assignment by output feedback in multivariable systems. Necessary and sufficient conditions for the closed-loop stabilization, eigenstructure assignment are presented in terms of a bilinear Sylvester equation, the solutions of which completely characterize the closed-loop eigenstructure problem with output feedback. Some preliminary results for the solution of this bilinear equation are presented.<
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